To see the other types of publications on this topic, follow the link: Gravitational field equation.
Journal articles on the topic 'Gravitational field equation'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 journal articles for your research on the topic 'Gravitational field equation.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.
1
DADHICH, N., and Z. YA TURAKULOV. "GRAVITATIONAL FIELD OF A ROTATING GRAVITATIONAL DYON." Modern Physics Letters A 17, no. 15n17 (2002): 1091–96. http://dx.doi.org/10.1142/s0217732302007508.
Full textAbstract:
We have obtained the general solution of the Einstein vacuum equation for the axially symmetric stationary metric in which both the Hamilton-Jacobi equation for particle motion and the Klein - Gordon equation are separable. It can be interpreted to describe the gravitational field of a rotating dyon, a particle endowed with both gravoelectric (mass) and gravomagnetic (NUT parameter) charges. Further, there also exists a duality relation between the two charges and the radial and the polar angle coordinates which keeps the solution invariant. The solution can however be transformed into the known Kerr - NUT solution indicating its uniqueness under the separability of equations of motion.
2
DEMİR, SÜLEYMAN, MURAT TANIŞLI, and TÜLAY TOLAN. "OCTONIC GRAVITATIONAL FIELD EQUATIONS." International Journal of Modern Physics A 28, no. 21 (2013): 1350112. http://dx.doi.org/10.1142/s0217751x13501121.
Full textAbstract:
Generalized field equations of linear gravity are formulated on the basis of octons. When compared to the other eight-component noncommutative hypercomplex number systems, it is demonstrated that associative octons with scalar, pseudoscalar, pseudovector and vector values present a convenient and capable tool to describe the Maxwell–Proca-like field equations of gravitoelectromagnetism in a compact and simple way. Introducing massive graviton and gravitomagnetic monopole terms, the generalized gravitational wave equation and Klein–Gordon equation for linear gravity are also developed.
3
Samokhvalov, S., and A. Hryshchenko. "THE LAWS OF MOTION IN GAUGE THEORIES OF GRAVITY." Collection of scholarly papers of Dniprovsk State Technical University (Technical Sciences) 1, no. 38 (2021): 116–22. http://dx.doi.org/10.31319/2519-2884.38.2021.14.
Full textAbstract:
The general theory of relativity (GR) states that the matter that generates the gravitational field cannot move arbitrarily, it must obey certain equations that follow from the equations of the gravitational field as conditions for their compatibility. In this article we analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Object: to consider the laws of motion in gauge theories of gravitation. Task to analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Conclusions: it is proved that the equation of an arbitrary gauge field of internal symmetry regardless of the specific type of its Lagrangian can be written both in the form of Einstein's equation and in superpotential form, i.e. as an expression of the total current of gauge charges through the superpotential determined by a specific type of Lagrangian that is, in the form of the Young-Mills equations. So this is a consequence of purely-symmetry theory. Also, a statement is proved in which the constraints on the equations of some fields, which follow from the assumption of the equations of motion for other fields. Research perspectives: nowadays, scientists register gravitational waves and analyze the conditions for their emission, and interest in the problem of motion has been renewed. Note that theories of gravity with higher derivatives of field variables in the Lagrangian of the gravitational field (for example, f(R)-theories) have become very popular in the present. Note that on the basis of the laws of motion of charged matter considered in the article in the gauge theory of gravity, it is possible to successfully further investigate the laws of motion in other theories of gravity, which can be useful in various areas of theoretical and experimental physics.
4
J.F., Omonile, Alexander A.O., John S., and Idachaba J.S. "Relativistic Mechanics in Gravitational Field within Oblate Spheroidal Coordinates Based upon Riemannian Geometry for Rotating Homogeneous Mass Distribution." Advanced Journal of Science, Technology and Engineering 3, no. 1 (2023): 51–62. http://dx.doi.org/10.52589/ajste-xmozirqs.
Full textAbstract:
The emergence of the geometrical theory of gravitation (general relativity) by Albert Einstein in his quest to unite special relativity and the Newtonian law of universal gravitation has led to several Mathematical approaches for the exact and analytical solution for all gravitational fields in nature. The first and the most famous analytical solution was the Schwarzchild’s which can be constructed by finding a mapping where the metric tensor takes a simple form i.e. the vanishing of the non-diagonal elements. In this paper, we construct exact solution of the Einstein geometrical gravitational field equation using Riemannian metric tensor called the golden metric tensor that was first developed by Howusu, in the year 2009, for the rotating homogeneous mass distribution within oblate Spheroidal Coordinates. The equations of motion for test particles in the Oblate Spheroidal Geometry were derived using the coefficient of affine connection. Then the law of conservation of momentum and energy are equivalently formulated using the generalized Lagrangian as compared to the analytical solution of the Schwarzchild’s gravitational field. We also derived the planetary equation of motion in the equatorial plane of the Oblate Spheroidal body for this gravitational field.
5
Winterberg, Friedwardt. "Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation." Zeitschrift für Naturforschung A 71, no. 1 (2016): 53–57. http://dx.doi.org/10.1515/zna-2015-0331.
Full textAbstract:
AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.
6
Arminjon, Mayeul. "Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation." Open Physics 14, no. 1 (2016): 395–409. http://dx.doi.org/10.1515/phys-2016-0045.
Full textAbstract:
AbstractAn alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes’ thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton’s second law. This implies Einstein’s geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell’s equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a “free” photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.
7
Fedosin, Sergey G. "Four-dimensional equation of motion for viscous compressible and charged fluid with regard to the acceleration field, pressure field and dissipation field." International Journal of Thermodynamics 18, no. 1 (2015): 13–24. https://doi.org/10.5541/ijot.5000034003.
Full textAbstract:
From the principle of least action the equation of motion for viscous compressible and charged fluid is derived. The viscosity effect is described by the 4-potential of the energy dissipation field, dissipation tensor and dissipation stress-energy tensor. In the weak field limit it is shown that the obtained equation is equivalent to the Navier-Stokes equation. The equation for the power of the kinetic energy loss is provided, the equation of motion is integrated, and the dependence of the velocity magnitude is determined. A complete set of equations is presented, which suffices to solve the problem of motion of viscous compressible and charged fluid in the gravitational and electromagnetic fields.
8
Weng, Zi-Hua. "Contrastive analysis of two energy gradients in the ultra-strong magnetic fields." International Journal of Modern Physics A 33, no. 35 (2018): 1850212. http://dx.doi.org/10.1142/s0217751x18502123.
Full textAbstract:
The paper aims to apply the complex-octonions to explore the variable gravitational mass and energy gradient of several particles in the external ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the algebra of quaternions to study the physical properties of electromagnetic fields. Some scholars follow up this method in the field theories. Nowadays, they employ the complex-octonions to analyze simultaneously the physical quantities of electromagnetic and gravitational fields, including the field potential, field strength, field source, linear momentum, angular momentum, torque, and force. When the octonion force is equal to zero, it is able to deduce eight independent equilibrium equations, especially the force equilibrium equation, precessional equilibrium equation, mass continuity equation, and current continuity equation. In the force equilibrium equation, the gravitational mass is variable. The gravitational mass is the sum of the inertial mass and a few tiny terms. These tiny terms will be varied with not only the fluctuation of field strength and of potential energy, but also the spatial dimension of velocity. The study reveals that it is comparatively untoward to attempt to measure directly the variation of these tiny terms of gravitational mass in the ultra-strong magnetic field. However it is not such difficult to measure the energy gradient relevant to the variation of these tiny terms of gravitational mass. In the complex-octonion space, the gravitational mass is a sort of variable physical quantity, rather than an intrinsic property of any physical object. And this inference is accordant with the academic thought of “the mass is not an intrinsic property any more” in the unified electroweak theory.
9
Lou Tai-Ping. "A covariant gravitational field equation including the contribution of gravitational field." Acta Physica Sinica 55, no. 4 (2006): 1602. http://dx.doi.org/10.7498/aps.55.1602.
Full text
10
Kohiyama, Noboru. "Gravitational waves derived from the elastic energy." Physics Essays 37, no. 4 (2024): 330–31. https://doi.org/10.4006/0836-1398-37.4.330.
Full textAbstract:
The Adams‐Williamson equations adeptly characterize the pressure distribution within Earth's interior, highlighting the role of pressure in storing elastic energy. This stored energy forms the basis for deriving the Newtonian gravitational field. The variability of the dielectric constant and electric charge (alongside magnetic permeability and magnetic charge) in response to gravitational field strength renders Maxwell's equations applicable within the context of a strong gravitational field. Intriguingly, the wave equation satisfied by the gravitational field can be derived from Maxwell's equations.
11
HUANG, XIN-BING. "UNIFICATION OF GRAVITATION, GAUGE FIELD AND DARK ENERGY." International Journal of Modern Physics A 21, no. 06 (2006): 1341–57. http://dx.doi.org/10.1142/s0217751x06028874.
Full textAbstract:
This paper is composed of two correlated topics: (1) unification of gravitation with gauge fields; (2) the coupling between the daor field and other fields and the origin of dark energy. After introducing the concept of "daor field" and discussing the daor geometry, we indicate that the complex daor field has two kinds of symmetry transformations. Hence the gravitation and SU(1, 3) gauge field are unified under the framework of the complex connection. We propose a first-order nonlinear coupling equation of the daor field, which includes the coupling between the daor field and SU(1, 3) gauge field and the coupling between the daor field and the curvature, and from which Einstein's gravitational equation can be deduced. The cosmological observations imply that dark energy cannot be zero, and which will dominate the doom of our Universe. The real part of the daor field self-coupling equation can be regarded as Einstein's equation endowed with the cosmological constant. It shows that dark energy originates from the self-coupling of the space–time curvature, and the energy–momentum tensor is proportional to the square of coupling constant λ. The dark energy density given by our scenario is in agreement with astronomical observations. Furthermore, the Newtonian gravitational constant G and the coupling constant ∊ of gauge field satisfy G = λ2∊2.
12
ABREU, E. M. C., C. PINHEIRO, S. A. DINIZ, and F. C. KHANNA. "ELECTROMAGNETIC WAVES, GRAVITATIONAL COUPLING AND DUALITY ANALYSIS." Modern Physics Letters A 21, no. 02 (2006): 151–58. http://dx.doi.org/10.1142/s0217732306019207.
Full textAbstract:
In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave equations are computed such that the electric field does not induce the magnetic field and vice versa. In a gravitational field, we analyze the Maxwell equations and the corresponding electromagnetic waves. A continuity equation is presented. A commutative and noncommutative analysis of the electromagnetic duality is described.
13
Razgovorov, N. N. "Dynamic treatment of gravitation. the interaction equation and equations of the gravitational field." Soviet Physics Journal 33, no. 5 (1990): 458–62. http://dx.doi.org/10.1007/bf00896090.
Full text
14
Oldani, Richard. "Relativistic Clocks and the Nature of Time." Journal of Physical Chemistry & Biophysics 13, no. 3 (2023): 4. https://doi.org/10.5281/zenodo.14603896.
Full textAbstract:
The interaction of an atomic clock with a gravitational field is analysed in detail in order to determine how the relativistic properties of time are manifested at the microscopic level. A differential equation of motion is first derived for the clock’s transitioning electron that is in compliance with the equivalence principle. Using Hamilton’s principle S Ldt = ∫ we work backwards from the differential equation to obtain an integral equation of motion, the time-integral of a Lagrangian, which is in conformance with relativity theory. It is postulated that no other equations are able to describe the simultaneous influence on clocks of two physical variables, velocity and gravitational potential. We conclude that the action minimum of a clock and Hamilton’s principle are synonymous.
15
Fedosin, Sergey G. "Two components of the macroscopic general field." Reports in Advances of Physical Sciences 1, no. 2 (2017): 1750002, 9 pages. https://doi.org/10.1142/S2424942417500025.
Full textAbstract:
The general field, containing all the macroscopic fields in it, is divided into the mass component, the source of which is the mass four-current, and the charge component, the source of which is the charge four-current. The mass component includes the gravitational field, acceleration field, pressure field, dissipation field, strong interaction and weak interaction fields, other vector fields. The charge component of the general field represents the electromagnetic field. With the help of the principle of least action we derived the field equations, the equation of the matter’s motion in the general field, the equation for the metric, the energy and momentum of the system of matter and its fields, and calibrated the cosmological constant. The general field components are related to the corresponding vacuum field components so that the vacuum field generates the general field at the macroscopic level.
16
Penner, A. Raymond. "A relativistic mass dipole gravitational theory and its connections with AQUAL." Classical and Quantum Gravity 39, no. 7 (2022): 075001. http://dx.doi.org/10.1088/1361-6382/ac5051.
Full textAbstract:
Abstract It will be shown that a gravitational theory based on there being an additional contribution to the gravitational field from mass dipoles leads to the same field equation that arises from the AQUAL formulation of MOND. However, unlike AQUAL, the mass dipole theory does not require a modification of Newtonian gravitational theory. In addition, both SR and linearized GR field equations will be derived for the mass dipole and AQUAL gravitational theories.
17
Kohiyama, Noboru. "Maxwell’s equations in the Newtonian gravitational field derived from the elastic energy." Physics Essays 37, no. 1 (2024): 80–82. http://dx.doi.org/10.4006/0836-1398-37.1.80.
Full textAbstract:
The Adams‐Williamson equation adeptly characterizes the pressure distribution within Earth’s interior, highlighting the role of pressure in storing elastic energy. This stored energy forms the basis for deriving the Newtonian gravitational field. Intriguingly, the variability of the dielectric constant and electric charge (alongside magnetic permeability and magnetic charge) in response to gravitational field strength renders Maxwell’s equations applicable within the context of a strong gravitational field.
18
Wei, Hai-Bo, Yi-Gu Chen, Hui Zheng, Zai-Dong Wang, Li-Qin Mi, and Zhong-Heng Li. "Perturbation analysis for massless spin fields in accelerating Kerr-Newman-(anti-)de Sitter black holes." Modern Physics Letters A 36, no. 24 (2021): 2150175. http://dx.doi.org/10.1142/s0217732321501753.
Full textAbstract:
We obtain the wave equation of the perturbation theory governing massless fields of spin 0, 1/2, 1, 3/2 and 2 in accelerating Kerr–Newman–(anti-)de Sitter black holes. We show that the wave equation is separable and the radial and angular equations can both be transformed into Heun’s equation. We approximate Heun’s equation and analyze the solution of radial function near the event horizon. It is worth pointing out that all the field equations collapse to a unique equation which means it can provide a possible way for the analog research between the gravitational field and those other fields.
19
Larson, D. J. "The quantum luminiferous aether." Physics Essays 37, no. 1 (2024): 9–30. http://dx.doi.org/10.4006/0836-1398-37.1.9.
Full textAbstract:
A solid, two-component, quantum luminiferous aether is proposed to exist. Simple postulates are hypothesized, along with some physical laws and assignments. Derivations then lead to the equations of electrodynamics (Maxwell’s equations and the Lorentz force equation), Newton’s law of universal gravitation, and to two field-masses. The theory is shown to successfully meet the classic tests of general relativity: calculations for the advance of the perihelia, the Shapiro effect, and the gravitational redshift agree with experiment, and the experimental result concerning the bending of light in gravitational fields is also understood. Additionally, gravitational waves are understood, and the first of the field-masses allows for an understanding of what is presently known as dark matter. A new approach to analyzing dense objects such as white dwarfs and neutron stars is discussed, and since the theory has no singularity, a replacement for black holes is suggested. Replacing relativity with an absolute, realist, and physical model returns us to a flat Euclidean space and a separate time. Absolute simultaneity enables understanding of quantum mechanics. The underlying philosophical grounding is discussed.
20
Asselmeyer-Maluga, Torsten, and Jerzy Król. "Dark Matter as Gravitational Solitons in the Weak Field Limit." Universe 6, no. 12 (2020): 234. http://dx.doi.org/10.3390/universe6120234.
Full textAbstract:
In this paper, we will describe the idea that dark matter partly consists of gravitational solitons (gravisolitons). The corresponding solution is valid for weak gravitational fields (weak field limit) with respect to a background metric. The stability of this soliton is connected with the existence of a special foliation and amazingly with the smoothness properties of spacetime. Gravisolitons have many properties of dark matter, such as no interaction with light but act on matter via gravitation. In this paper, we showed that the gravitational lensing effect of gravisolitons agreed with the lensing effect of usual matter. Furthermore, we obtained the same equation of state w=0 as matter.
21
Soldateschi, Jacopo, and Niccolò Bucciantini. "Detectability of Continuous Gravitational Waves from Magnetically Deformed Neutron Stars." Galaxies 9, no. 4 (2021): 101. http://dx.doi.org/10.3390/galaxies9040101.
Full textAbstract:
Neutron stars are known to contain extremely powerful magnetic fields. Their effect is to deform the shape of the star, leading to the potential emission of continuous gravitational waves. The magnetic deformation of neutron stars, however, depends on the geometry and strength of their internal magnetic field as well as on their composition, described by the equation of state. Unfortunately, both the configuration of the magnetic field and the equation of state of neutron stars are unknown, and assessing the detectability of continuous gravitational waves from neutron stars suffers from these uncertainties. Using our recent results relating the magnetic deformation of a neutron star to its mass and radius—based on models with realistic equations of state currently allowed by observational and nuclear physics constraints—and considering the Galactic pulsar population, we assess the detectability of continuous gravitational waves from pulsars in the galaxy by current and future gravitational waves detectors.
22
Morozov, Valery Borisovich. "Approximate solution of the new gravitational field equation." Parana Journal of Science and Education 10, no. 3 (2024): 1–4. https://doi.org/10.5281/zenodo.11283129.
Full textAbstract:
Based on the numerical solution of the new gravitational field equation, an approximate component of themetric of the gravitational field of a point mass is obtained. Unlike the solution to the Einstein equation, thissolution does not contain singularities.
23
Cremaschini, Claudio, and Massimo Tessarotto. "The Wave-Front Equation of Gravitational Signals in Classical General Relativity." Symmetry 12, no. 2 (2020): 216. http://dx.doi.org/10.3390/sym12020216.
Full textAbstract:
In this paper the dynamical equation for propagating wave-fronts of gravitational signals in classical general relativity (GR) is determined. The work relies on the manifestly-covariant Hamilton and Hamilton–Jacobi theories underlying the Einstein field equations recently discovered (Cremaschini and Tessarotto, 2015–2019). The Hamilton–Jacobi equation obtained in this way yields a wave-front description of gravitational field dynamics. It is shown that on a suitable subset of configuration space the latter equation reduces to a Klein–Gordon type equation associated with a 4-scalar field which identifies the wave-front surface of a gravitational signal. Its physical role and mathematical interpretation are discussed. Radiation-field wave-front solutions are pointed out, proving that according to this description, gravitational wave-fronts propagate in a given background space-time as waves characterized by the invariant speed-of-light c. The outcome is independent of the actual shape of the same wave-fronts and includes the case of gravitational waves which are characterized by an eikonal representation and propagate in a generic curved space-time along a null geodetics. The same waves are shown: (a) to correspond to the geometric-optics limit of the same curved space-time solutions; (b) to propagate in a flat space-time as plane waves with constant amplitude; (c) to display also the corresponding form of the wave-front in curved space-time. The result is consistent with the theory of the linearized Einstein field equations and the existence of gravitational waves achieved in such an asymptotic regime. Consistency with the non-linear Trautman boundary-value theory is also displayed.
24
Karim, Munawar. "Auto-stabilized electron." International Journal of Modern Physics A 35, no. 02n03 (2020): 2040024. http://dx.doi.org/10.1142/s0217751x20400242.
Full textAbstract:
We include effects of self-gravitation in the self-interaction of single electrons with the electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the [Formula: see text]-vector - the upper limit is finite. The inward pressure of the self-gravitating field balances the outward pressure of self-interaction. Both pressures are generated by self-interactions of the electron with two fields - the vacuum electromagnetic field and the self-induced gravitational field. Specifically we demonstrate that gravitational effects must be included to stabilize the electron. We use the Einstein equation to perform an exact calculation of the bare mass and electron radius. We find a close-form solution. We find the electron radius [Formula: see text]m, where [Formula: see text] is the Planck length educed from first principles. We find that the electromagnetic and gravitational fields merge at [Formula: see text] GeV in terms of the Planck mass [Formula: see text]. The unified field depends on [Formula: see text] and [Formula: see text] alone, independent of [Formula: see text]; the unified field is continuous. Renormalisation is accomplished by requiring continuity of the interior and exterior metrics at [Formula: see text].
25
Reginatto, M. "On classical gravitational corrections to the functional Schrödinger equation." Journal of Physics: Conference Series 2883, no. 1 (2024): 012010. http://dx.doi.org/10.1088/1742-6596/2883/1/012010.
Full textAbstract:
Abstract A full theory of quantum gravity is not yet available, and an approximation in which spacetime remains classical while matter is described by quantum fields is often physically and computationally appropriate. It is therefore of interest to investigate hybrid systems which describe the interaction of classical gravity with quantum matter. Such systems may provide valuable clues relevant to the search of a quantum theory of gravity. Furthermore, one should also consider the possibility that the gravitational field may not be quantum in nature; in that case, it would become necessary to search for a consistent hybrid description. It is known that the Wheeler-De Witt equation with coupling to quantum fields results in quantum gravitational corrections to the functional Schrödinger equation. A similar result can be obtained for some hybrid models where a classical gravitational field interacts with quantum matter fields. I use the approach of ensembles on configuration space to look at a hybrid model where matter is in the form of a quantized scalar field and determine the corresponding classical gravitational corrections to the functional Schrödinger equation.
26
De Bernardis, Enrico, and Giorgio Riccardi. "Dynamics of a bubble rising in gravitational field." Communications in Applied and Industrial Mathematics 7, no. 1 (2016): 48–67. http://dx.doi.org/10.1515/caim-2016-0018.
Full textAbstract:
AbstractThe rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.
27
Dirkes, Alain. "Gravitational waves — A review on the theoretical foundations of gravitational radiation." International Journal of Modern Physics A 33, no. 14n15 (2018): 1830013. http://dx.doi.org/10.1142/s0217751x18300132.
Full textAbstract:
In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating [Formula: see text]-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.
28
Fedosin, Sergey G. "About the Cosmological Constant, Acceleration Field, Pressure Field and Energy." Jordan Journal of Physics 9, no. 1 (2016): 1–30. https://doi.org/10.5281/zenodo.889304.
Full textAbstract:
Based on the condition of relativistic energy uniqueness, the calibration of the cosmological constant was performed. This allowed to obtain the corresponding equation for the metric and to determine the generalized momentum, the relativistic energy, momentum and mass of the system, as well as the expressions for the kinetic and potential energies. The scalar curvature at an arbitrary point of the system equaled zero, if the matter is absent at this point; the presence of a gravitational or electromagnetic field is enough for the space-time curvature. Four-potentials of the acceleration field and pressure field, as well as tensor invariants determining the energy density of these fields, were introduced into the Lagrangian in order to describe the system’s motion more precisely. The structure of the Lagrangian used is completely symmetrical in form with respect to the four-potentials of gravitational, electromagnetic, acceleration and pressure fields. The stress-energy tensors of the gravitational, acceleration and pressure fields are obtained in explicit form. Each of them can be expressed through the corresponding field vector and additional solenoidal vector. A description of the equations of acceleration and pressure fields is provided.
29
Wanchat, Sujate, Ratchaphon Suntivarakorn, Sujin Wanchat, Kitipong Tonmit, and Pongpun Kayanyiem. "A Parametric Study of a Gravitation Vortex Power Plant." Advanced Materials Research 805-806 (September 2013): 811–17. http://dx.doi.org/10.4028/www.scientific.net/amr.805-806.811.
Full textAbstract:
This study is the analysis and design of a basin structure which has the ability to form a gravitational vortex stream. Such a high velocity water vortex stream can possibly be used as an alternative energy resource. In this study we are interested in the formation of a water vortex stream by gravitation, which is a new technique used in the field of hydro power engineering. The advantage of this method for electrical generation is the capability of producing energy using low heads of 0.7 to 3 meters. It can be applied in a low head micro hydro power plant. The governing equations are the Navier-Stokes equations. The SIMPLE method was adopted to solve the discretized equation. The flow fields in the flume, under different incoming flow conditions and basin configurations, were numerically simulated using the software ANSYS Fluent. The studies investigated parameters which affect the velocity vector flow field, which include 1) Outlet diameter at the bottom center of basin 2) Gravitational vortex head and 3) Flow rate. Computational fluid dynamics is used to simulate the vector flow field. The tangential and radial velocity distribution is used to determine the suitable turbine blade for testing. A gravitational vortex power plant model is created to investigate electrical power output.
30
Siagian, Ruben Cornelius, Lulut Alfaris, Arip Nurahman, Aldi Cahya Muhammad, Ukta Indra Nyuswantoro, and Budiman Nasution. "Separation of Variables Method in Solving Partial Differential Equations and Investigating the Relationship between Gravitational Field Tensor and Energy-Momentum Tensor in Einstein's Theory of Gravity." Kappa Journal 7, no. 2 (2023): 343–51. http://dx.doi.org/10.29408/kpj.v7i2.20921.
Full textAbstract:
This research delves into the study of partial differential equations (PDEs) and gravitational fields in spacetime. It focuses on solving PDEs using the Separation of Variables method and explores the relationship between the gravitational field tensor and the energy-momentum tensor, leading to the final equation for the gravitational field tensor. The research also investigates Einstein's theory of gravity and the energy-momentum tensor integral, providing the general solution for the gravitational potential and its implications. Additionally, the mean integration of the gravitational wave tensor is analyzed, yielding an expression for the tensor strain of gravitational waves over an infinitely long period. The components of the gravitational wave tensor and their effect on gravitational sources are examined. Furthermore, the propagation of electromagnetic fields in spacetime is studied using the Retarded Green's Function. The primary objectives of this research are to understand and explore mathematical techniques for solving PDEs and analyzing gravitational fields and their interactions in spacetime. The integration of multiple theoretical concepts related to PDEs, gravitational fields, and electromagnetic fields enhances our understanding of fundamental physics principles. This contributes to the advancement of theoretical physics and opens avenues for potential practical applications, such as gravitational wave detection and electromagnetic field propagation in complex media. In conclusion, this research provides valuable insights into fundamental physics principles and fosters a deeper understanding of their interconnections and implications
31
Inan, Nader, Ahmed Farag Ali, Kimet Jusufi, and Abdelrahman Yasser. "Graviton mass due to dark energy as a superconducting medium-theoretical and phenomenological aspects." Journal of Cosmology and Astroparticle Physics 2024, no. 08 (2024): 012. http://dx.doi.org/10.1088/1475-7516/2024/08/012.
Full textAbstract:
Abstract It is well known that the cosmological constant term in the Einstein field equations can be interpreted as a stress tensor for dark energy. This stress tensor is formally analogous to an elastic constitutive equation in continuum mechanics. As a result, the cosmological constant leads to a “shear modulus” and “bulk modulus” affecting all gravitational fields in the universe. The form of the constitutive equation is also analogous to the London constitutive equation for a superconductor. Treating dark energy as a type of superconducting medium for gravitational waves leads to a Yukawa-like gravitational potential and a massive graviton within standard General Relativity. We discuss a number of resulting phenomenological aspects such as a screening length scale that can also be used to describe the effects generally attributed to dark matter. In addition, we find a gravitational wave plasma frequency, index of refraction, and impedance. The expansion of the universe is interpreted as a Meissner-like effect as dark energy causes an outward “expulsion” of space-time similar to a superconductor expelling a magnetic field. The fundamental cause of these effects is interpreted as a type of spontaneous symmetry breaking of a scalar field. There is an associated chemical potential, critical temperature, and an Unruh-Hawking effect associated with the formulation.
32
Kremer, Gilberto M. "Theory and applications of the relativistic Boltzmann equation." International Journal of Geometric Methods in Modern Physics 11, no. 02 (2014): 1460005. http://dx.doi.org/10.1142/s0219887814600056.
Full textAbstract:
In this work, two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external electromagnetic fields in special relativity. In this case the Fourier and Ohm laws are derived and the corresponding transport coefficients are obtained. In the other a relativistic gas under the influence of the Schwarzschild metric is studied. It is shown that the heat flux in Fourier's law in the presence of gravitational fields has three contributions, the usual dependence on the temperature gradient, and two relativistic contributions, one of them associated with an acceleration and another to a gravitational potential gradient. Furthermore, it is shown that the transport coefficient of thermal conductivity decreases in the presence of a gravitational field. The dependence of the temperature field in the presence of a gravitational potential is also discussed.
33
Drivotin, Oleg I. "The Einstein equation solution inside a ball with uniform density." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 20, no. 1 (2024): 4–9. http://dx.doi.org/10.21638/11701/spbu10.2024.101.
Full textAbstract:
A great number of solutions of the Einstein field equation are known. They describe the gravitational field in the empty space-time, in the space-time with electromagnetic field and for a ball filled with a liquid under pressure. The present work is devoted to gravitational field generated by some mass distribution. One of the simplest cases is considered, when mass is uniformly distributed inside a ball and is not moving. The boundary problem for the Einstein equation is formulated. Solution outside the ball is the Schwartzschild solution in vacuum. The coordinates at which the Schwartzschild solution is written are different from the coordinates used in equations for components of the metric tensor inside the ball. Relations between internal and external coordinates are found on the ball surface. They allow to use the Schwartzschild solution for formulation of boundary conditions for internal solution. The solution of the boundary problem is found for the case of weak field. This solution can be used as an example in the analysis of laws of conservation for the gravitational field, in which interaction of mass with field generated by the mass gives a contribution to momentum and energy of the gravitational field.
34
Chakraborty, Sumanta. "Field Equations for Lovelock Gravity: An Alternative Route." Advances in High Energy Physics 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/6509045.
Full textAbstract:
We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.
35
Sharif, M., and Zahid Ahmad. "ADDENDUM: "GRAVITATIONAL PERFECT FLUID COLLAPSE WITH COSMOLOGICAL CONSTANT"." Modern Physics Letters A 22, no. 38 (2007): 2947–48. http://dx.doi.org/10.1142/s0217732307025972.
Full text
36
Yuan, Tony. "Gravitational fields and gravitational waves." Physics Essays 35, no. 2 (2022): 208–19. http://dx.doi.org/10.4006/0836-1398-35.2.208.
Full textAbstract:
The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: Is there a linear relationship between gravity and velocity? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? What is the spatial distribution of gravitational waves? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton's gravitational equation through the influence of gravitational waves?
37
ALDROVANDI, R., V. C. DE ANDRADE, and J. G. PEREIRA. "GRAVITOMAGNETIC MOMENTS OF THE FUNDAMENTAL FIELDS." International Journal of Modern Physics A 15, no. 19 (2000): 2971–78. http://dx.doi.org/10.1142/s0217751x00002123.
Full textAbstract:
The quadratic form of the Dirac equation in a Riemann space–time yields a gravitational gyromagnetic ratio κS=2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κS=1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square-root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.
38
Kuptsov, Stanislav, Mikhail Ioffe, Sergey Manida, and Sergey Paston. "Weak Field Limit for Embedding Gravity." Universe 8, no. 12 (2022): 635. http://dx.doi.org/10.3390/universe8120635.
Full textAbstract:
We study a perturbation theory for embedding gravity equations in a background for which corrections to the embedding function are linear with respect to corrections to the flat metric. The remaining arbitrariness after solving the linearized field equations is fixed by an assumption that the solution is static in the second order. A nonlinear differential equation is obtained, which allows for finding the gravitational potential for a spherically symmetric case if a background embedding is given. An explicit form of a spherically symmetric background parameterized by one function of radius is proposed. It is shown that this function can be chosen in such a way that the gravitational potential is in a good agreement with the observed distribution of dark matter in a galactic halo.
39
Bulus, Timothy, Chifu E. Ndikilar, Halliru Ibrahim, and Dayyabu Tafida. "General Relativistic Study of Motion of Comets Particles Elliptical Gravitational Field." Physics Access 05, no. 01 (2025): 73–75. https://doi.org/10.47514/phyaccess.2025.5.1.008.
Full textAbstract:
Comets are small bodies consisting of aggregates of ice mixed with rock and dust. They are usually influenced by galactic forces and stellar encounters, and may have contributed to the formation of ice giants and transport gases across the solar system. Their orbits vary widely, and their frozen water sublimates around 3 AU, forming a coma, though some remain active beyond this distance. In this study, the line element in the gravitational field due to a static and ellipsoidal isolated gravitating mass point was used to study the motion of comets, and the relativistic equation of motion of an ellipsoidal mass was obtained via the metric tensor, affine connections and geodesics equation. The results show that the explicit equations of comets along the equatorial plane are second-order differential equations similar to reported results in the literature for different gravitational fields.
40
Pinheiro, Mario J. "Extended Field Interactions in Poisson’s Equation Revision." Applied Sciences 14, no. 5 (2024): 1833. http://dx.doi.org/10.3390/app14051833.
Full textAbstract:
This investigation introduces a new variational approach to refining Poisson’s equation, enabling the inclusion of a broader spectrum of physical phenomena, particularly in the emerging fields of spintronics and the analysis of resonant structures. The innovative formulation extends the traditional capabilities of Poisson’s equation, offering a nonlocal extension to classical theories of gravitation and opening new directions for energy conversion and enhanced communication technologies. By introducing a novel geometric structure, ω˜, into the equation, a deeper understanding of electrostatic potentials is achieved, and the intricate dynamics of the gravitational potential in systems characterized by radial vorticity fluctuations are illuminated. Furthermore, the research elucidates the generation of longitudinal electromagnetic waves and resonant phenomena within dusty plasma media, thereby contributing to the methodological advances in the study of nonequilibrium systems. These theoretical advances have the potential to transform the understanding of complex physical systems and open up opportunities for significant technological achievements across a range of scientific sectors.
41
Agrawal, Aniket. "Non-Gaussianity of inflationary gravitational waves from the field equation." International Journal of Modern Physics D 28, no. 02 (2019): 1950036. http://dx.doi.org/10.1142/s0218271819500366.
Full textAbstract:
We demonstrate equivalence of the in–in formalism and Green’s function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, [Formula: see text], agrees with the results obtained previously using the in–in formalism exactly. Characterizing non-Gaussianity of the fluctuations using the ratio [Formula: see text] in the equilateral configuration, where [Formula: see text] is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green’s function, reproducing the results from in–in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.
42
Osetrin, Konstantin E., Vladimir Y. Epp, and Altair E. Filippov. "Exact Model of Gravitational Waves and Pure Radiation." Symmetry 16, no. 11 (2024): 1456. http://dx.doi.org/10.3390/sym16111456.
Full textAbstract:
An exact non-perturbative model of a gravitational wave with pure radiation is constructed. It is shown that the presence of dust matter in this model contradicts Einstein’s field equations. The exact solution to Einstein’s equations for gravitational wave and pure radiation is obtained. The trajectories of propagation and the characteristics of radiation are found. For the considered exact model of a gravitational wave, a retarded time equation for radiation is obtained. The obtained results are used to construct an exact model of gravitational wave and pure radiation for the Bianchi type IV universe.
43
Fedosin, Sergey G. "The concept of the general force vector field." OALib Journal 3 (March 7, 2016): 1–15. https://doi.org/10.4236/oalib.1102459.
Full textAbstract:
A hypothesis is suggested that the fields associated with macroscopic bodies, such as classical electromagnetic and gravitational fields, acceleration field, pressure field, dissipation field, strong interaction field and weak interaction field, are the manifestations of a single general field. Using the generalized four-velocity as the four-potential of the general field, with the help of the principle of least action it is shown that each of these seven fields contributes linearly to the formation of the total four-force density. The general field equations, equation of the particles’ motion in this field, equation for the metric and the system’s energy are determined. It should be noted that the stress-energy tensor of the general field includes not only the stress-energy tensors of these seven fields, but also the cross terms with the products of various field strengths. As a result, the energy and momentum of the system with several fields can differ from the classical values, not taking into account such cross terms in the general field energy and momentum.
44
Sabbar, Ali Nadhim, and G. N. Shikin. "The Effect of Cosmic Vacuum on the Properties of Scalar Field." International Letters of Chemistry, Physics and Astronomy 61 (November 2015): 58–62. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.61.58.
Full textAbstract:
The thesis explains the effect of cosmic vacuum of gravitational field on properties of scalar field equation. In the space-time plane, the scalar field equation has periodic solution φx,y,z,t=Acos (kx±ωt). Consideration the cosmic vacuum of gravitational field (using De Sitter metric in its synchronization time) the equation of scalar field will have accurate solution in form of Beseel function. By using the asymptotic representation, the periodic solution (t→±∞) will vanish. The scalar field equation when t→+∞ will decrease regularly, and when t→-∞ it will increasing fluctuate.
45
Sabbar, Ali Nadhim, and G. N. Shikin. "The Effect of Cosmic Vacuum on the Properties of Scalar Field." International Letters of Chemistry, Physics and Astronomy 61 (November 3, 2015): 58–62. http://dx.doi.org/10.56431/p-l2l41c.
Full textAbstract:
The thesis explains the effect of cosmic vacuum of gravitational field on properties of scalar field equation. In the space-time plane, the scalar field equation has periodic solution φx,y,z,t=Acos (kx±ωt). Consideration the cosmic vacuum of gravitational field (using De Sitter metric in its synchronization time) the equation of scalar field will have accurate solution in form of Beseel function. By using the asymptotic representation, the periodic solution (t→±∞) will vanish. The scalar field equation when t→+∞ will decrease regularly, and when t→-∞ it will increasing fluctuate.
46
Sorokin, N. A. "Earth's gravity field parameters determination by the space geodesy dynamical approach." Geodesy and Cartography 919, no. 1 (2017): 7–12. http://dx.doi.org/10.22389/0016-7126-2017-919-1-7-12.
Full textAbstract:
The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.
47
Vyblyi, Yu P., and O. G. Kurguzova. "Static solutions in the Freund – Nambu scalar-tensor theory of gravitation." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 4 (2021): 464–69. http://dx.doi.org/10.29235/1561-2430-2021-57-4-464-469.
Full textAbstract:
Herein, the system of Einstein equations and the equation of the Freund – Nambu massless scalar field for static spherically symmetric and axially symmetric fields are considered. It is shown that this system of field equations decouples into gravitational and scalar subsystems. In the second post-Newtonian approximation, the solutions for spherically symmetric and slowly rotating sources are obtained. The application of the obtained solutions to astrophysical problems is discussed.
48
Frolov, Alexei M. "On the Hamiltonian and Hamilton–Jacobi equations for metric gravity." Canadian Journal of Physics 98, no. 4 (2020): 405–12. http://dx.doi.org/10.1139/cjp-2019-0217.
Full textAbstract:
The closed system of Hamiltonian equations is derived for all tensor components of a free gravitational field gαβ and corresponding momenta πγδ in metric general relativity. The Hamilton–Jacobi equation for a free gravitational field gαβ is also derived and discussed. In general, all methods and procedures based on the Hamiltonian and Hamilton–Jacobi approaches are very effective in actual applications to many problems known in metric general relativity.
49
Ayala Oña, Roger I., Darya P. Kislyakova, and Tatyana P. Shestakova. "On the Appearance of Time in the Classical Limit of Quantum Gravity." Universe 9, no. 2 (2023): 85. http://dx.doi.org/10.3390/universe9020085.
Full textAbstract:
A possible solution of the problem of time in the Wheeler–DeWitt quantum geometrodynamics is that time appears within a semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved spacetime with quantum-gravitational corrections. In the present paper, we study the semiclassical limit in the case of a closed isotropic model with a scalar field decomposed into modes. We analyse calculations made within frameworks of three approaches. The first approach was proposed by Kiefer and Singh. Since the Wheeler–DeWitt equation does not contain a time derivative, it is constructed by means of a special mathematical procedure, a time variable being a parameter along a classical trajectory of gravitational field. The second method was suggested in the paper of Maniccia and Montani, who introduced the Kuchař–Torre reference fluid as an origin of time. Furthermore, the third is the extended phase space approach to the quantisation of gravity. In this approach, the temporal Schrodinger equation is argued to be more fundamental than the Wheeler–DeWitt equation, and there is no problem of time. Time is introduced due to fixing a reference frame of a certain observer, who can register the macroscopic consequences of quantum gravitational phenomena in the Very Early Universe. To go to the semiclassical limit, the Born–Oppenheimer approximation for gravity is used. In each of the approaches, in the order of O(1/M), a temporal Schrödinger equation for matter fields in curved spacetime with quantum gravitational corrections is obtained. However, equations and corrections are different in various approaches, and the results depend on the additional assumptions made within the scopes of these approaches.
50
Sharif, M., and Sobia Sadiq. "Study of gravitational decoupled anisotropic solution." International Journal of Modern Physics D 28, no. 16 (2019): 2040004. http://dx.doi.org/10.1142/s0218271820400040.
Full textAbstract:
This paper formulates the exact static anisotropic spherically symmetric solution of the field equations through gravitational decoupling. To accomplish this work, we add a new gravitational source in the energy–momentum tensor of a perfect fluid. The corresponding field equations, hydrostatic equilibrium equation as well as matching conditions are evaluated. We obtain the anisotropic model by extending the known Durgapal and Gehlot isotropic solution and examined the physical viability as well as the stability of the developed model. It is found that the system exhibits viable behavior for all fluid variables as well as energy conditions and the stability criterion is fulfilled.