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Academic literature on the topic 'Gravitational field equation'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

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Journal articles on the topic "Gravitational field equation"

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Dissertations / Theses on the topic "Gravitational field equation"

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Buchman, Luisa T. "A hyperbolic tetrad approach to numerical relativity /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5451.

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Düll, Maximilian [Verfasser], and Björn Malte [Akademischer Betreuer] Schäfer. "Gravitational closure of matter field equations General theory & symmetrization / Maximilian Düll ; Betreuer: Björn Malte Schäfer." Heidelberg : Universitätsbibliothek Heidelberg, 2020. http://d-nb.info/1213902509/34.

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Sidhu, Steve. "Conformal field theory and black hole physics." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Physics and Astronomy, c2012, 2012. http://hdl.handle.net/10133/3109.

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This thesis reviews the use of 2-dimensional conformal field theory applied to gravity, specifically calculating Bekenstein-Hawking entropy of black holes in (2+1) dimensions. A brief review of general relativity, Conformal Field Theory, energy extraction from black holes, and black hole thermodynamics will be given. The Cardy formula, which calculates the entropy of a black hole from the AdS/CFT duality, will be shown to calculate the correct Bekenstein-Hawking entropy of the static and rotating BTZ black holes. The first law of black hole thermodynamics of the static, rotating, and charged-rotating BTZ black holes will be verified.<br>vii, 119 leaves : ill. ; 29 cm

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Gaset, Rifà Jordi. "A multisymplectic approach to gravitational theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/620740.

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The theories of gravity are one of the most important topics in theoretical physics and mathematical physics nowadays. The classical formulation of gravity uses the Hilbert-Einstein Lagrangian, which is a singular second-order Lagrangian; hence it requires a geometric theory for second-order field theories which leads to several difficulties. Another standard formulation is the Einstein-Palatini or Metric-Affine, which uses a singular first order Lagrangian. Much work has been done with the aim of establishing the suitable geometrical structures for describing classical field theories. In particular, the multisymplectic formulation is the most general of all of them and, in recent years, some works have considered a multisymplectic approach to gravity. This formulation allows us to study and better understand several inherent characteristics of the models of gravity. The aim of this thesis is to use the multisymplectic formulation for first and second-order field theories in order to obtain a complete covariant description of the Lagrangian and Hamiltonian formalisms for the Einstein-Hilbert and the Metric-Affine models, and explain their characteristics; in particular: order reduction, constraints, symmetries and gauge freedom. Some properties of multisymplectic field theories have been developed in order to study the models. We have established the constraints generated by the projectability of the Poincaré-Cartan form. These constraints are related to the fact that the higher order velocities are strong gauge vector fields. The concept of gauge freedom for field theories also has been analyzed. We propose to use the term "gauge'' to refer to the non-regularity of the Poincaré-Cartan form. Therefore, the multiple solutions are characterized by two sources: the gauge related one, arising from gauge symmetries and related to the non-regularity; and the non-gauge related one, which arises exclusively from field theories. We studied in detail two models of gravity: the Einstein-Hilbert model and the Metric-Affine (or Einstein-Palatini) model. In both cases, a covariant Hamiltonian multisymplectic formalism has been presented. In every situation, we find the final submanifold where solutions exist, and we explicitly write all semi-holonomic multivector fields solution of the field equations. The natural Lagrangian symmetries are presented aswell. Furthermore, we emphasize different aspects in each model: The Einstein-Hilbert model is a singular second order field theory which, as a consequence of its non-regularity, it is equivalent to a regular first order theory. For this model we have presented the unified Lagrangian-Hamiltonian formalism. We have also considered the presence of energy-matter sources and we show how some relevant geometrical and physical characteristics of the theory depend on the source's type. The Metric-Affine model is a singular first order field theory which has a gauge symmetry. We recover and study this gauge symmetry, showing that there are no more. The constraints of the system are presented and analysed. Using the gauge freedom and the constraints, we establish the geometric relation between the Einstein-Palatini and the Einstein-Hilbert models, including the relation between the holonomic solutions in both formalisms. We also present a Hamiltonian model involving only the connection which is equivalent to the Hamiltonian Metric-Affine formalism.<br>Les teories de la gravetat són un dels temes més importants en física teòrica i física matemàtica avui en dia. La formulació clàssica de la gravetat utilitza el Lagrangià de Hilbert-Einstein, el qual és un Lagrangià singular de segon ordre; per tant requereix una teoria geomètrica per teories de camp de segon ordre, que comporten diverses dificultats. Una altra formulació estàndard és la d'Einstein-Palatini o Mètrica-Afí, la qual utilitza un Lagrangià singular de primer ordre. S'ha treballat molt per establir les estructures geomètriques adients per descriure teories de camps clàssiques. Particularment, la formulació multisimplèctica és la més general de totes i, recentment alguns treballs han considerat la gravetat des de un punt de vista multisimplèctic. Aquesta formulació ens permet estudiar i entendre millor diverses característiques inherents dels models gravitatoris. L'objectiu d'aquesta tesi és utilitzar la formulació multisimplèctica per a teories de camps de primer i segon ordre per obtenir una descripció covariant completa dels formalismes Lagrangià i Hamiltonià per als models d'Einstein-Hilbert i Mètrica-Afí, i explicar les seves característiques. Concretament: reducció de l'ordre, restriccions, simetries i llibertat gauge. Algunes propietats de les teories de camps multisimplèctiques han estat desenvolupades per estudiar els models. S'han establert les restriccions generades per la projectabilitat de la forma de Poincaré-Cartan. Aquestes restriccions tenen relació amb el fet que les velocitats d'ordre superior són camps vectorials gauge forts. El concepte de llibertat gauge per a teories de camps també ha estat analitzat. Es proposa la utilització del terme "gauge" per fer referència a la no regularitat de les formes de Poincaré-Cartan. Per tant, les múltiples solucions es caracteritzen a partir de dues fonts: la relativa al gauge, que està relacionada amb la no regularitat, i altres fonts no relacionades amb el gauge que són exclusives de teories de camps. S'ha estudiat en detall dos models de gravetat: el model d'Einstein-Hilbert i el de Mètrica-Afí (o Einstein-Palatinti). En ambdós casos s'ha presentat una formulació covariant multisimplèctica Hamiltoniana. En tots els casos trobem la subvarietat final on les solucions existeixen, i escrivim explícitament tots els camps multivectorials sem-holònoms solució de les equacions de camp. També presentem les simetries Lagrangianes naturals. A més emfatitzem aspectes diferents en cada model: El model d'Einstein-Hilbert és una teoria de camp singular de segon ordre, la qual, com a conseqüència de la seva no regularitat, és equivalent a una teoria regular de primer ordre. Per aquest model hem presentat el formalisme unificat Lagrangià-Hamiltonià. També hem considerat la presència de fonts d'energia-matèria i es mostra com algunes característiques físiques i geomètriques rellevants de la teoria depenen del tipus de font. El model Mètrica-Afí és una teoria de camps singular de primer ordre que té una simetria gauge. Es recupera i s'estudia aquesta simetria gauge mostrant que és única. Les lligadures del sistema són presentades i analitzades. Utilitzant la llibertat gauge i les lligadures, s'estableix la relació geomètrica entre els models d'Einstein-Palatini i d'Einstein-Hilbert, inclosa la relació entre les solucions holònomes en ambdós formalismes. També es presenta un model Hamiltonià, que conté únicament la connexió, equivalent al formalisme Mètrica-Afí Hamiltonià

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Van, der Walt Petrus Johannes. "Numerical relativity on cosmological past null cones." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1002959.

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The observational approach to cosmology is the endeavour to reconstruct the geometry of the Universe using only data that is theoretically verifiable within the causal boundaries of a cosmological observer. Using this approach, it was shown in [36] that given ideal cosmological observations, the only essential assumption necessary to determine the geometry of the Universe is a theory of gravity. Assuming General Relativity, the full set of Einstein field equations (EFEs) can be used to reconstruct the geometry of the Universe using direct observations on the past null cone (PNC) as initial conditions. Observationally and theoretically this is a very ambitious task and therefore, current developments have been restricted to spherically symmetric dust models while only relaxing the usual assumption of homogeneity in the radial direction. These restricted models are important for the development of theoretical foundations and also useful as verification models since they avoid the circularity of verifying what has already been assumed. The work presented in this thesis is the development of such a model where numerical relativity (NR) is used to simulate the observable universe. Similar to the work of Ellis and co-workers [36], a reference frame based on the PNC is used. The reference frame used here, however, is based on that of the characteristic formalism of NR, which has developed for calculating the propagation of gravitational waves. This provides a formalism that is well established in NR, making the use of existing algorithms possible. The Bondi-Sachs coordinates of the characteristic formalism is, however, not suitable for calculations beyond the observer apparent horizon (AH) since the diameter distance used as a radial coordinate becomes multi-valued when the cosmological PNC reconverges in the history of a universe, smaller in the past. With this taken into consideration, the Bondi-Sachs characteristic formalism is implemented for cosmology and the problem approaching the AH is investigated. Further developments address the limitations approaching the AH by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced with an affine parameter. The model is derived with a cosmological constant Λ incorporated into the EFEs where Λ is taken as a parameter of the theory of gravity rather than as a matter source term. Similar to the conventional characteristic formalism, this model consists of a system of differential equations for numerically evolving the EFEs as a characteristic initial value problem (CIVP). A numerical code implemented for the method has been found to be second order convergent. This code enables simulations of different models given identical data on the initial null cone and provides a method to investigate their physical consistency within the causally connected region of our current PNC. These developments closely follow existing 3D schemes developed for gravitational wave simulations, which should make it natural to extend the affine CIVP beyond spherical symmetric simulations. The developments presented in this thesis is an extended version of two papers published earlier.

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Keane, Aidan J. "Liouville's equation and radiative acceleration in general relativity." Thesis, University of Glasgow, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301358.

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Da, Silva Caroline Dos Santos. "Cosmic strings and scalar tensor gravity." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4577/.

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This thesis is concerned with the study of cosmic strings. We studied the values for the Higgs mass and string coupling for which the gravitational effect of an infinite cosmic string in the context of the Einstein theory is not only locally but also globally weak. We conclude this happens for strings formed at scales less or equal to the Planck one with Higgs mass being less or equal to the boson vectorial mass. Then we examined the metric of an isolated self-gravitating abelian-Higgs vortex in dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton. We looked for solutions in both massless and massive dilaton gravity. We compared our results to existing metrics for strings in Einstein and .Jordan-Brans-Dicke theories. We explored the generalisation of Bogomolnyi arguments for our vortices and commented on the effects on test particles. We then included the presence of an axion field and examined the metric of an isolated self-gravitating axionic-dilatonic string. Finally we studied dilatonic strings through black hole solutions in string theory. We concluded that the horizon of non-extreme charged black holes supports the long-range fields of the Nielsen-Olesen string that can be considered as black hole hair and whose gravitational effect is in general the production of a conical deficit into the metric of the black hole background. We also concluded that the effect of the dilaton on the horizon of these black holes is to generate an additional charge.

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Tseng, Hung-Hsu, and 曾鴻旭. "On the Equation of Motion of a Dirac Particle in Gravitational Field and its Gyro-Gravitational Ratio." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/27247840164427638432.

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碩士<br>國立清華大學<br>物理學系<br>89<br>In this thesis,we write down the Dirac equation with the third-order expension of the metric tensor.The curvature effects give out the Gyro-Gravitational Ratio. Via three succesive Foldy-Wouthuysen transformation, we obtain the Dirac equation in weak field, slow motion limit; and further,calculate the geodesic deviation equation, compare with Papapetrou equation. Finally,we will discuss the Gyro-Gravitational Ratio.

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Malik, Tuhin. "Equation of state for dense matter from finite nuclei to neutron star mergers." Doctoral thesis, 2019. http://hdl.handle.net/10316/94981.

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Documentos apresentados no âmbito do reconhecimento de graus e diplomas estrangeiros<br>Equation of state (EOS) of dense matter has been constrained from the experimental data available on the properties of finite nuclei and neutron stars. Towards this purpose, a diverse set of nuclear energy density functionals based on relativistic and non-relativistic mean field models have been employed. These EOSs are so chosen that they are consistent with the bulk properties of the finite nuclei. The values of various nuclear matter parameters which predominantly govern the behaviour of the EOS are determined through their correlations with the properties of the neutron stars such as radii, tidal deformability and maximum mass of the neutron stars. The nuclear matter parameters considered are incompressibility, symmetry energy and their density derivatives which appear in the expansion of the EOS around the saturation density. The radii and tidal deformability of the neutron star with the canonical mass display strong correlations with the linear combinations of slopes of the incompressibility and symmetry energy coefficients. Similar correlations with the curvature of the symmetry energy coefficient are also obsvered indicating that the properties of the neutron stars are sensitive to the high density behaviour of the symmetry energy. It is also shown that the giant resonances in nuclei are instrumental in limiting the tidal deformability parameter and the radius of a neutron star in somewhat narrower bounds. The outcomes of the present thesis is important in view of the fact that the accurate values of the various neutron star observables as considered are expected to be available in near future.

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Mahlatji, Matsimele Ngwalodi. "Some models of relativistic radiating stars." Thesis, 2012. http://hdl.handle.net/10413/10616.

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In this dissertation we study radiating stars in strong gravitational elds. We generate new classes of exact solutions to the Einstein eld equations and the boundary condition applicable to radiating relativistic stars. The model of a radiating star in general relativity, matching to the Vaidya exterior spacetime, is reviewed. The boundary condition is converted to a Riccati equation and we consider both cases involving geodesic and non-geodesic particle trajectories. We present the metrics found previously. We rst solve the boundary condition for the geodesic case and nd the gravitational potentials which are expanding and shearing. This is a new result. Secondly the boundary condition is analysed for the non-geodesic case and we seek new gravitational potentials which are accelerating, expanding and shearing. We are able to identify only geodesic solutions for this second case; this appears to be a new class of models. The solutions found are presented in terms of elementary functions which are helpful in studying the physical properties. The new solutions found cannot be categorised in existing classes of known solutions; they are examples of a new generic class di erent from previous studies. The matter variables of the model are generated .<br>Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.

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Books on the topic "Gravitational field equation"

1

Jefimenko, Oleg D. Causality, electromagnetic induction, and gravitation: A different approach to the theory of electromagnetic and gravitational fields. 2nd ed. Electret Scientific Co., 2000.

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Jefimenko, Oleg D. Causality, electromagnetic induction, and gravitation: A different approach to the theory of electromagnetic and gravitational fields. Electret Scientific Co., 1992.

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T, Chruściel Piotr, and Królak Andrzej, eds. Mathematics of gravitation. Polish Academy of Sciences, Institute of Mathematics, 1997.

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Chruściel, Piotr T., and Helmut Friedrich, eds. The Einstein Equations and the Large Scale Behavior of Gravitational Fields. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7953-8.

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Kh, Huleihil, and Leibowitz E, eds. Gauge fields. World Scientific, 1989.

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United States. National Aeronautics and Space Administration., ed. General equations for the motions of ice crystals and water drops in gravitational and electric fields. Institut d'aeronomie spatiale de Belgique, 1988.

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P, Hsu J., and Fine Dana, eds. 100 years of gravity and accelerated frames: The deepest insights of Einstein and Yang-Mills. World Scientific, 2005.

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Chruściel, Piotr T. The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity. Birkhäuser Basel, 2004.

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Griffiths, J. B. Colliding plane waves in general relativity. Clarendon Press, 1991.

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Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. American Mathematical Society, 2016.

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Book chapters on the topic "Gravitational field equation"

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Roy, Sisir. "Einstein Equation for Gravitational Field." In Statistical Geometry and Applications to Microphysics and Cosmology. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5230-3_6.

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Gasperini, Maurizio. "The Dirac Equation in a Gravitational Field." In Theory of Gravitational Interactions. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49682-5_13.

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Gasperini, Maurizio. "The Dirac Equation in a Gravitational Field." In Theory of Gravitational Interactions. Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2691-9_13.

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Renn, Jürgen, and Tilman Sauer. "Heuristics and Mathematical Representation in Einstein’s Search for a Gravitational Field Equation." In The Expanding Worlds of General Relativity. Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-0639-2_3.

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Freire-Torres, Mario, and Jaime Carpio. "Contribution to Mathematical Modeling and Numerical Simulation of Welding Processes." In Proceedings of the XV Ibero-American Congress of Mechanical Engineering. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-38563-6_4.

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AbstractThe present work describes a mathematical model for the numerical simulation of the welding process. Initially, the domain Ω is solid to which the heat is released in certain areas. This heat increases the temperature of the solid, and when the fusion temperature is reached, the phase change occurs. At the fusion temperature, there is a mixture between liquid and solid (modelled as a porous medium); above this temperature mentioned; we will find only liquid. Natural convection currents can occur in the liquid due to buoyancy induced by the gravitational field. In order to reproduce all the phenomenology described, the mathematical model will be based on the energy conservation equation, expressed in terms of enthalpy, together with the mass and momentum conservation equations to determine the velocity of the fluid. The numerical resolution of the equations will be carried out with a Lagrange-Galerkin formulation in a finite element framework, where a temporal discretization BDF2 scheme will be used.

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Cercignani, Carlo, and Gilberto Medeiros Kremer. "Boltzmann Equation in Gravitational Fields." In The Relativistic Boltzmann Equation: Theory and Applications. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8165-4_12.

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Gasperini, Maurizio. "The Einstein Equations for the Gravitational Field." In Theory of Gravitational Interactions. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-49682-5_7.

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Gasperini, Maurizio. "The Einstein Equations for the Gravitational Field." In Theory of Gravitational Interactions. Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2691-9_7.

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Blanchet, Luc. "Post-Newtonian Gravitational Radiation." In Einstein’s Field Equations and Their Physical Implications. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46580-4_3.

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Beig, Robert, and Bernd Schmidt. "Time-Independent Gravitational Fields." In Einstein’s Field Equations and Their Physical Implications. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46580-4_5.

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Conference papers on the topic "Gravitational field equation"

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Havare, A. Kemal, Ali Havare, and Kenan Söǧüt. "The (1+1)-D Duffin-Kemmer-Petiau Equation In A Constant Gravitational Field." In SIXTH INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. AIP, 2007. http://dx.doi.org/10.1063/1.2733079.

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Krylova, N., and V. Red'kov. "Dirac particle in gravitational field of black hole with Newman-Unti-Tamburino parameter." In Modern astronomy: from the Early Universe to exoplanets and black holes. Special Astrophysical Observatory of the Russian Academy of Sciences, 2024. https://doi.org/10.26119/vak2024.013.

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We study the quantum-mechanical problem of a spin 1/2 particle in gravitational field of the black hole with Newman-Unti-Tamburino (NUT) parameter. Separation of the variables has been performed in the Dirac equation. The system of angular equations has been solved analytically in terms of hypergeometric functions. The quantization condition for the angular parameter is derived. In the massless case, the radial system is reduced to separate systems of two first-order equations which are solved in terms of the confluent Heun functions. Generalized tortoise-like coordinate is introduced, and expressions for the effective complex-valued potentials are found. We may expect that the present analysis can permit us to elucidate the physical interpretation for the Newman-Unti-Tamburino metric. The question arises about possible existence of the Hawking-like radiation in this model.

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Gao, Zhi-Fu, Hao Shan, Hui Wang, and Na Wang. "Evolutions of magnetic field and spin-down of pulsars." In XIAMEN-CUSTIPEN WORKSHOP ON THE EQUATION OF STATE OF DENSE NEUTRON-RICH MATTER IN THE ERA OF GRAVITATIONAL WAVE ASTRONOMY. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5117823.

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Biswal, S. K. "Effects of ɸ0-meson on the EOS of hyperon star in a relativistic mean field model". У XIAMEN-CUSTIPEN WORKSHOP ON THE EQUATION OF STATE OF DENSE NEUTRON-RICH MATTER IN THE ERA OF GRAVITATIONAL WAVE ASTRONOMY. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5117821.

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Wang, Yongjia, Yunxiao Ye, and Qingfeng Li. "Mean-field potential effects in the cumulants of baryons from central Au+Au collision at Elab= 1.23 GeV/nucleon." In XIAMEN-CUSTIPEN WORKSHOP ON THE EQUATION OF STATE OF DENSE NEUTRON-RICH MATTER IN THE ERA OF GRAVITATIONAL WAVE ASTRONOMY. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5117825.

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Ikegai, Tomoki, Wataru Yoshimori, Shoichi Yasuda, and Shusaku Harada. "Wireless Measurement of Fluid Force in Liquid-Solid Flow by Lagrangian Sensor Particle." In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ajkfluids2015-31322.

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We have developed a “sensor particle”, which is a Lagrangian sensor system for real-time measurement of the force acting on a particle moving freely in fluid flow. The sensor particle is composed of an acceleration sensor, magnetometer, microcomputer, wireless module and cells. The built-in acceleration sensor detects the acceleration of particle at each instant of time. However, the signals contain both dynamic and static (gravitational) accelerations. Therefore we applied the external magnetic field oriented in the gravitational direction in order to identify the attitude of the sensor particle and to remove the gravitational acceleration from the measured signals. Consequently, we can obtain the force acting on a particle moving in fluid at each time through the equation of the motion. We have applied our system to oscillatory liquid flow with particle assemblage to obtain the basic knowledge on unsteady fluid force in a multi-particle system.

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Khulief, Y. A., S. Bashmal, and F. A. Al-Sulaiman. "Coupled Torsional Vibrations in Drilling Systems." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80489.

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The contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A dynamic model of the drillstring including both drillpipe and drillcollars is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach together with the finite element method. The model accounts for the gyroscopic effect, the torsional/bending inertia coupling, the axial/bending geometric nonlinear coupling, and the stiffening effect due to the gravitational force field. Reduced order modal form of the dynamic equations is obtained using complex modal transformation. The developed model is integrated into a computational scheme to calculate time-response of the drillstring due to torsional excitations.

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Khulief, Y. A., F. A. Al-Sulaiman, and S. Bashmal. "Modeling of Stick-Slip in Multibody Drilling Systems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84225.

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Drillstring vibration is one of the major causes for a deteriorated drilling performance. Field experience revealed that it is crucial to understand the complex vibrational mechanisms experienced by a drilling system in order to better control its functional operation and improve its performance. Stick-slip oscillations due to contact between the drilling bit and formation is known to excite severe torsional and axial vibrations in the drillstring. A multibody dynamic model of the drilling system including the drillpipes, drillcollars, and the rotary drive is formulated. The equation of motion of the rotating drillstring is derived using Lagrangean approach in conjunction with the finite element method. The model accounts for the gyroscopic effect, the inertia coupling, the effect of the gravitational force field, and the stick-slip interaction forces. Explicit expressions of the finite element inertia coupling and axial stiffening matrices are derived using a consistent mass formulation. Modal transformations are invoked to obtain a reduced order modal form of the dynamic equations. The developed model is integrated into a computational scheme to calculate time-response of the drillstring system in the presence of stick-slip excitations.

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Popowicz, Z. "Integrability of the N=3 supersymmetric KdV equation." In Particles, fields and gravitation. AIP, 1998. http://dx.doi.org/10.1063/1.57101.

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Rodrigues, Fabio Grangeiro, Waldyr Alves Rodrigues Jr., and Roldão da Rocha. "The Maxwell and Navier-Stokes equations that follow from Einstein equation in a spacetime containing a Killing vector field." In THE SIXTH INTERNATIONAL SCHOOL ON FIELD THEORY AND GRAVITATION-2012. AIP, 2012. http://dx.doi.org/10.1063/1.4756974.

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Reports on the topic "Gravitational field equation"

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Xing, Yulong, and Chi-Wang Shu. High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields. Defense Technical Information Center, 2011. http://dx.doi.org/10.21236/ada557672.

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Lynch, James F. A digital Higgs universe and the flow of time. Woods Hole Oceanographic Institution, 2024. http://dx.doi.org/10.1575/1912/70830.

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Theoretically considering velocities greater than c implies considering an observer’s past and extends the overall analysis into the complex plane. By using a series of rotations by i in the complex plane at the Planck scale, one can create a four-lobed structure of “instants of time,” which together with considering matter and antimatter in the lobes and the +/- sense of the rotation, leads to a Higgs field representation of spacetime. A metric is developed for this system as well as a generalized spacetime interval. It is shown that the Friedmann Equations are consistent with our “Higgs Cosmology” if generalized to a set of gravitationally coupled equations that connect the forward and backward going solutions. Simple solutions for the forward and backward going universes are presented and are shown to be consistent with the backward solution providing both inflation and a “cosmological constant” type of dark energy. Dark matter is discussed and is separately hypothesized to be due to the mass of the four “Higgs sectors” as seen by an observer in our universe. A digital, stroboscopic and holographic universe picture emerges which can also be viewed as a beginning theory of quantum gravity at the Planck scale.

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