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Journal articles on the topic 'Spacetime curvature'

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Published: 2 June 2025

Last updated: 13 July 2025

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Mallick, Sahanous, and Uday Chand De. "Spacetimes admitting W2-curvature tensor." International Journal of Geometric Methods in Modern Physics 11, no. 04 (2014): 1450030. http://dx.doi.org/10.1142/s0219887814500303.

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The object of this paper is to study spacetimes admitting W2-curvature tensor. At first we prove that a W2-flat spacetime is conformally flat and hence it is of Petrov type O. Next, we prove that if the perfect fluid spacetime with vanishing W2-curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has vanishing acceleration vector and expansion scalar and the perfect fluid always behaves as a cosmological constant. It is also shown that in a perfect fluid spacetime of constant scalar curvature with divergence-free W2-curvature tensor, the energy-momentum tensor is of Codazzi type and the possible local cosmological structure of such a spacetime is of type I, D or O.

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Ali, Mohabbat, Mohd Vasiulla, and Meraj Ali Khan. "Analysis of W3 Curvature Tensor in Modified Gravity and Its Cosmological Implications." Symmetry 17, no. 4 (2025): 542. https://doi.org/10.3390/sym17040542.

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In this study, we investigated the geometric and physical implications of the W3 curvature tensor within the framework of f(R,G) gravity. We found the sufficient conditions for W3 flat spacetimes with constant scalar curvature to be de Sitter (R>0) or Anti-de Sitter (R<0) models. The properties of isotropic spacetime in the modified gravity framework were also investigated. Furthermore, we explored spacetimes with a divergence-free W3 curvature tensor. The necessary and sufficient condition for a W3 Ricci recurrent and parallel spacetime to transform into an Einstein spacetime was determined. Finally, we analyzed the role of the W3 curvature tensor in black hole thermodynamics within f(R,G) gravity.

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De, Krishnendu, Changhwa Woo, and Uday De. "Geometric and physical characterizations of a spacetime concerning a novel curvature tensor." Filomat 38, no. 10 (2024): 3535–46. https://doi.org/10.2298/fil2410535d.

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In this article, we introduce ?-concircular curvature tensor, a new tensor that generalizes the concircular curvature tensor. At first, we produce a few fundamental geometrical properties of ?-concircular curvature tensor and pseudo ?-concircularly symmetric manifolds and provide some inter-esting outcomes. Besides, we investigate ?-concircularly flat spacetimes and establish some significant results about Minkowski spacetime, RW-spacetime, and projective collineation. Moreover, we show that if a ?-concircularly flat spacetime admits a Ricci bi-conformal vector field, then it is either Petrov type N or conformally flat. Moreover, we consider pseudo ? concircularly symmetric spacetime with Codazzi type of Ricci tensor and prove that the spacetime is of Petrov types I, D or O and the spacetime turns into a RW spacetime. Also, we establish that in a pseudo ? concircularly symmetric spacetime with harmonic ?-concircular curvature tensor, the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent. At last, we produce a non-trivial example to validate the existence of4 a (PCS) manifold.

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Salman, Mohammad, Musavvir Ali, and Mohd Bilal. "Curvature Inheritance Symmetry in Ricci Flat Spacetimes." Universe 8, no. 8 (2022): 408. http://dx.doi.org/10.3390/universe8080408.

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In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, if Ricci flat spacetimes are not of Petrov type N, and admit curvature inheritance symmetries, then the only existing symmetries are conformal motions. We also prove that the only Ricci flat spacetime that admits a proper curvature inheritance symmetry and is of Petrov type other than N is the flat spacetime. Next, we find that the vacuum pp-waves of Petrov type N if admit curvature inheritance symmetry, then conformal motion implies homothetic motion.

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Khan, Amir Sultan, Israr Ali Khan, Saeed Islam, and Farhad Ali. "Noether symmetry analysis for novel gravitational wave-like spacetimes and their conservation laws." Modern Physics Letters A 35, no. 28 (2020): 2050234. http://dx.doi.org/10.1142/s021773232050234x.

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The phenomena-like Hawking radiation, the collapse of black holes, and neutron stars decrease the curvature of spacetime continuously with the passage of time. The time conformal factor adds some curvature to nonstatic spacetime. In this article, some novel classes of nonstatic plane-symmetric spacetimes are explored by introducing a time conformal factor in the exact plane-symmetric spacetimes in such a way that their symmetric structure remains conserved. This technique re-scales the energy contents of the corresponding spacetimes, which comes with a re-scaled part in each spacetime. The invariant quantities corresponding to the Noether symmetries are also calculated.

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CABALLERO, MAGDALENA, ALFONSO ROMERO, and RAFAEL M. RUBIO. "COMPLETE CMC SPACELIKE SURFACES WITH BOUNDED HYPERBOLIC ANGLE IN GENERALIZED ROBERTSON–WALKER SPACETIMES." International Journal of Geometric Methods in Modern Physics 07, no. 06 (2010): 961–78. http://dx.doi.org/10.1142/s0219887810004658.

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Complete spacelike surfaces with constant mean curvature (CMC) and bounded hyperbolic angle in Generalized Robertson–Walker (GRW) spacetimes, obeying certain natural curvature assumptions, are studied. This boundedness assumption arises as a natural extension of the notion of bounded hyperbolic image of a spacelike surface in the 3-dimensional Lorentz–Minkowski spacetime. The results obtained apply to complete CMC spacelike surfaces lying between two spacelike slices in an GRW spacetime, in the steady state spacetime and in a static GRW spacetime. As an application, uniqueness and non-existence theorems for certain CMC spacelike surface differential equations in a wide family of open GRW spacetimes are given.

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Mofarreh, Fatemah, Krishnendu De та Uday De. "Characterizations of a spacetime admitting ψ-conformal curvature tensor". Filomat 37, № 30 (2023): 10265–74. http://dx.doi.org/10.2298/fil2330265m.

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In this paper, we introduce ?-conformal curvature tensor, a new tensor that generalizes the conformal curvature tensor. At first, we deduce a few fundamental geometrical properties of ?-conformal curvature tensor and pseudo ?-conharmonically symmetric manifolds and produce some interesting outcomes. Moreover, we study ?-conformally flat perfect fluid spacetimes. As a consequence, we establish a number of significant theorems about Minkowski spacetime, GRW-spacetime, projective collineation. Moreover, we show that if a?-conformally flat spacetime admits a Ricci bi-conformal vector field, then it is either conformally flat or of Petrov type N. At last, we consider pseudo?conformally symmetric spacetime admitting harmonic ?-conformal curvature tensor and prove that the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent and also, the Ricci collineation and matter collineation are equivalent.

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De, Uday Chand, and Young Jin Suh. "Some characterizations of Lorentzian manifolds." International Journal of Geometric Methods in Modern Physics 16, no. 01 (2019): 1950016. http://dx.doi.org/10.1142/s0219887819500166.

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Generalized Robertson–Walker (GRW) spacetime is the generalization of the Robertson–Walker (RW) spacetime and a further generalization of GRW spacetime is the twisted spacetime. In this paper, we generalize the results of the paper [C. A. Mantica, Y. J. Suh and U. C. De, A note on generalized Robertson–Walker spacetimes, Int. J. Geom. Methods Mod. Phys. 13 (2016), Article Id: 1650079, 9 pp., doi: 101142/s0219887816500791 ]. We prove that a Ricci simple Lorentzian manifold with vanishing quasi-conformal curvature tensor is a RW spacetime. Further, we prove that a Ricci simple Lorentzian manifold with harmonic quasi-conformal curvature tensor is a GRW spacetime. As a consequence, we obtain several corollaries. Finally, we have cited some examples of the obtained results.

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Mofarreh, Fatemah, and De Chan. "Characterizations of twisted spacetime." Filomat 35, no. 14 (2021): 4871–78. http://dx.doi.org/10.2298/fil2114871m.

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The object of the present paper is to characterize pseudo Ricci symmetric twisted spacetimes. At first it is shown that a pseudo Ricci symmetric twisted spacetime is a GRW spacetime. Next, we obtain a necessary and sufficient condition for a pseudo Ricci symmetric twisted spacetime to be a perfect fluid spacetime. It is also proved that a pseudo Ricci symmetric twisted spacetime is perfect fluid, provided the conformal curvature tensor is divergence free. Moreover, we investigate shear and vorticity vector fields of such type of spacetimes and pointed out its implications towards the evolution of the Early Universe. Finally, we study conformally flat (PRS)n spacetimes.

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Ali, Musavvir, Mohammad Salman, and Mohd Bilal. "Conharmonic Curvature Inheritance in Spacetime of General Relativity." Universe 7, no. 12 (2021): 505. http://dx.doi.org/10.3390/universe7120505.

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The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV.

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Ahsan, Zafar, and Musavvir Ali. "Curvature tensor for the spacetime of general relativity." International Journal of Geometric Methods in Modern Physics 14, no. 05 (2017): 1750078. http://dx.doi.org/10.1142/s0219887817500785.

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In the differential geometry of certain [Formula: see text]-structures, the role of [Formula: see text]-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing [Formula: see text]-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing [Formula: see text]-tensor have also been considered. The divergence of [Formula: see text]-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved [Formula: see text]-tensor represents either an Einstein space or a Friedmann-Robertson-Walker cosmological model.

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Triantafyllopoulos, Alkiviadis, Emmanuel Kapsabelis, and Panayiotis C. Stavrinos. "Raychaudhuri Equations, Tidal Forces, and the Weak-Field Limit in Schwarzshild–Finsler–Randers Spacetime." Universe 10, no. 1 (2024): 26. http://dx.doi.org/10.3390/universe10010026.

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In this article, we study the form of the deviation of geodesics (tidal forces) and the Raychaudhuri equation in a Schwarzschild–Finsler–Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by considering the structure of a Lorentz tangent bundle of spacetime and, in particular, the kind of the curvatures in generalized metric spaces where there is more than one curvature tensor, such as Finsler-like spacetimes. In these cases, the concept of the Raychaudhuri equation is extended with extra terms and degrees of freedom from the dependence on internal variables such as the velocity or an anisotropic vector field. Additionally, we investigate some consequences of the weak-field limit on the spacetime under consideration and study the Newtonian limit equations which include a generalization of the Poisson equation.

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Suh, Young, Pradip Majhi, and De Chand. "On mixed quasi-Einstein spacetimes." Filomat 32, no. 8 (2018): 2707–19. http://dx.doi.org/10.2298/fil1808707s.

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The object of the present paper is to study mixed quasi-Einstein spacetimes, briefly M(QE)4 spacetimes. First we prove that every Z Ricci pseudosymmetric M(QE)4 spacetimes is a Z Ricci semisymmetric spacetime. Then we study Z flat spacetimes. Also we consider Ricci symmetric M(QE)4 spacetimes and among others we prove that the local cosmological structure of a Ricci symmetricM(QE)4 perfect fluid spacetime can be identified as Petrov type I, DorO. We show that such a spacetime is the Robertson-Walker spacetime. Moreover we deal with mixed quasi-Einstein spacetimes with the associated generators U and V as concurrent vector fields. As a consequence we obtain some important theorems. Among others it is shown that a perfect fluid M(QE)4 spacetime of non zero scalar curvature with the basic vector field of spacetime as velocity vector field of the fluid is of Segr?e characteristic [(1,1,1),1]. Also we prove that a M(QE)4 spacetime can not admit heat flux provided the smooth function b is not equal to the cosmological constant k. This means that such a spacetime describe a universe which has already attained thermal equilibrium. Finally, we construct a non-trivial Lorentzian metric of M(QE)4.

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Hobill, D., and W. Guo. "Cosmology without dark energy: Weyl curvature solutions." Canadian Journal of Physics 86, no. 4 (2008): 571–77. http://dx.doi.org/10.1139/p08-002.

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To reconcile recent observations that the cosmological expansion has a positive acceleration with the standard Friedmann–Lemaitre–Robertson–Walker models of our Universe, as yet unseen sources of energy and (or) momentum are required for an explanation. This is due to the particular nature of spacetimes that assume homogeneity and isotropy where the curvature of the spacetime is linked to the energy-momentum content of the matter and fields in the spacetime. It is shown that more general cosmological models where Weyl (or vacuum) curvature is present can produce effects that might be responsible for the observed acceleration and other phenomena.PACS Nos.: 95.30.sf, 95.36.+x, 98.80.jk

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Price, Richard H. "Spatial curvature, spacetime curvature, and gravity." American Journal of Physics 84, no. 8 (2016): 588–92. http://dx.doi.org/10.1119/1.4955154.

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Mattingly, Brandon, Abinash Kar, Matthew Gorban, et al. "Curvature Invariants for the Accelerating Natário Warp Drive." Particles 3, no. 3 (2020): 642–59. http://dx.doi.org/10.3390/particles3030042.

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A process for using curvature invariants is applied to evaluate the accelerating Natário warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Natário spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants the Ricci scalar, r1, r2, and w2. The invariant plots demonstrate how each curvature invariant evolves over the parameters of time, acceleration, skin depth and radius of the warp bubble. They show that the Ricci scalar has the greatest impact of the invariants on the surrounding spacetime. They also reveal key features of the Natário warp bubble such as a flat harbor in the center of it, a dynamic wake, and the internal structures of the warp bubble.

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KOWALSKI-GLIKMAN, JERZY, and GIACOMO ROSATI. "RELATIVE LOCALITY IN CURVED SPACETIME." Modern Physics Letters A 28, no. 22 (2013): 1350101. http://dx.doi.org/10.1142/s0217732313501010.

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In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a nontrivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are present. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (de Sitter) spacetimes, relying on their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with κ-Poincaré momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.

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Shaikh, Absos Ali, Akram Ali, Ali H. Alkhaldi, and Dhyanesh Chakraborty. "Curvature properties of Nariai spacetimes." International Journal of Geometric Methods in Modern Physics 17, no. 03 (2020): 2050034. http://dx.doi.org/10.1142/s0219887820500346.

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This paper is concerned with the study of the geometry of (charged) Nariai spacetime, a topological product spacetime, by means of covariant derivative(s) of its various curvature tensors. It is found that on this spacetime the condition [Formula: see text] is satisfied and it also admits the pseudosymmetric type curvature conditions [Formula: see text] and [Formula: see text]. Moreover, it is 4-dimensional Roter type, [Formula: see text]-quasi-Einstein and generalized quasi-Einstein spacetime. The energy–momentum tensor is expressed explicitly by some 1-forms. It is worthy to see that a generalization of such topological product spacetime proposes to exist with a class of generalized recurrent type manifolds which is semisymmetric. It is observed that the rank of [Formula: see text], [Formula: see text], of Nariai spacetime (NS) is 0 whereas in case of charged Nariai spacetime (CNS) it is 2, which exhibits that effects of charge increase the rank of Ricci tensor. Also, due to the presence of charge in CNS, it gives rise to the proper pseudosymmetric type geometric structures.

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De, Krishnendu, and Uday De. "Perfect fluid spacetimes obeying certain restrictions on the energy-momentum tensor." Filomat 37, no. 11 (2023): 3483–92. https://doi.org/10.2298/fil2311483d.

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This paper is concerned with the study of a perfect fluid spacetime endowed with the various forms of the energy-momentum tensor T. We establish that a perfect fluid spacetime endowed with covariant constant energy-momentum tensor represents a dark matter era or the matter content is a perfect fluid spacetime with vanishing vorticity; whereas a perfect fluid spacetime endowed with Codazzi type of T represents a dark matter era or the expansion scalar vanishes, provided ?1 remains invariant under the velocity vector field ?. Also, we show that a perfect fluid spacetime with pseudo-symmetric energymomentum tensor represents a dark matter era or a phantom era, provided the velocity vector field annihilates the curvature tensor. Moreover, we characterize T-recurrent and weakly-T symmetric perfect fluid spacetimes with Killing velocity vector field and acquired that the perfect fluid spacetimes represent a radiation era in the first case and a stiff matter for the last one.

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Rovenski, Vladimir. "Einstein-Hilbert type action on spacetimes." Publications de l'Institut Math?matique (Belgrade) 103, no. 117 (2018): 199–210. http://dx.doi.org/10.2298/pim1817199r.

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The mixed gravitational field equations have been recently introduced for codimension one foliated manifolds, e.g. stably causal and globally hyperbolic spacetimes. These Euler-Lagrange equations for the total mixed scalar curvature (as analog of Einstein-Hilbert action) involve a new kind of Ricci curvature (called the mixed Ricci curvature). In the work, we derive Euler-Lagrange equations of the action for any spacetime, in fact, for a pseudo-Riemannian manifold endowed with a non-degenerate distribution. The obtained equations are presented in the classical form of Einstein field equation with the new Ricci type curvature instead of Ricci curvature

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De, Uday, and Fatemah Mofarreh. "Impact of concircular curvature tensor in f(R*)-gravity." Filomat 38, no. 30 (2024): 10529–37. https://doi.org/10.2298/fil2430529d.

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This paper concerns with the characterization of a spacetime and f (R*)-gravity endowed with concircular curvature tensor. We prove that a concircularly flat perfect fluid spacetime is either a de- Sitter spacetime or locally isometric to Minkowski spacetime. Moreover, it is established that a perfect fluid spacetime admitting harmonic concircular curvature tensor represents a Robertson-Walker spacetime. Finally, we examine the impact of concircularly flat perfect fluid spacetime solutions in two forms of f (R*)-gravity.

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De, Uday Chand, Sameh Shenawy, Abdallah Abdelhameed Syied, and Nasser Bin Turki. "Conformally Flat Pseudoprojective Symmetric Spacetimes in f R , G Gravity." Advances in Mathematical Physics 2022 (March 25, 2022): 1–7. http://dx.doi.org/10.1155/2022/3096782.

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Sufficient conditions on a pseudoprojective symmetric spacetime PPS n whose Ricci tensor is of Codazzi type to be either a perfect fluid or Einstein spacetime are given. Also, it is shown that a PPS n is Einstein if its Ricci tensor is cyclic parallel. Next, we illustrate that a conformally flat PPS n spacetime is of constant curvature. Finally, we investigate conformally flat PPS 4 spacetimes and conformally flat PPS 4 perfect fluids in f R , G theory of gravity, and amongst many results, it is proved that the isotropic pressure and the energy density of conformally flat perfect fluid PPS 4 spacetimes are constants and such perfect fluid behaves like a cosmological constant. Further, in this setting, we consider some energy conditions.

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Ali, Musavvir, Naeem Pundeer, and Young Suh. "Proper semiconformal symmetries of spacetimes with divergence-free semiconformal curvature tensor." Filomat 33, no. 16 (2019): 5191–98. http://dx.doi.org/10.2298/fil1916191a.

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In the present paper, the symmetries admitted by semiconformal curvature tensor in semiconformally symmetric spacetime have been studied and we show that a four-dimensional spacetime admitting a proper semiconformal symmetry is semiconformally flat or of the Petrov type N. It is also shown that a four-dimensional spacetime with divergence-free semiconformal curvature tensor admitting a proper semiconformal symmetry is locally of the Petrov type O or has four distinct principal null directions. In both the cases, we found that if the spacetime admits an infinitesimal semiconformal Killing vector field then the scalar curvature of the spacetime vanishes.

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Battista, Emmanuele, Giampiero Esposito, Paolo Scudellaro, and Francesco Tramontano. "Riemann curvature of a boosted spacetime geometry." International Journal of Geometric Methods in Modern Physics 13, no. 01 (2016): 1650002. http://dx.doi.org/10.1142/s021988781650002x.

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The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild–de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild–de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s [Formula: see text] distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all [Formula: see text] terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.

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BEESHAM, A. "HIGHER DIMENSIONAL INHOMOGENEOUS DUST COLLAPSE AND COSMIC CENSORSHIP." International Journal of Modern Physics A 17, no. 20 (2002): 2747. http://dx.doi.org/10.1142/s0217751x02011746.

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The singularity theorems of general relativity predict that gravitational collapse finally ends up in a spacetime singularity1. The cosmic censorship hypothesis (CCH) states that such a singularity is covered by an event horizon2. Despite much effort, there is no rigorous formulation or proof of the CCH. In view of this, examples that appear to violate the CCH and lead to naked singularities, in which non-spacelike curves can emerge, rather than black holes, are important to shed more light on the issue. We have studied several collapse scenarios which can lead to both situations3. In the case of the Vaidya-de Sitter spacetime4, we have shown that the naked singularities that arise are of the strong curvature type. Both types of singularities can also arise in higher dimensional Vaidya and Tolman-Bondi spacetimes, but black holes are favoured in some sense by the higher dimensions. The charged Vaidya-de Sitter spacetime also exhibits both types of singularities5.

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WANAS, M. I., and SAMAH A. AMMAR. "SPACETIME STRUCTURE AND ELECTROMAGNETISM." Modern Physics Letters A 25, no. 20 (2010): 1705–21. http://dx.doi.org/10.1142/s0217732310032883.

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Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first Lagrangian gives rise to pure gravity, while the theory constructed using the second Lagrangian gives rise to both gravity and electromagnetism. The two theories are constructed in a version of absolute parallelism geometry in which both curvature and torsion are, simultaneously, nonvanishing. One single geometric object, W-tensor, reflecting the properties of curvature and torsion, is defined in this version and is used to construct the second theory. The main conclusion is that a necessary condition for geometric representation of electromagnetism is the presence of a nonvanishing torsion in the geometry used.

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Ali, Farhad, Muhammad Asif Jan, Wali Khan Mashwani, Rashida Adeeb Khanum, and Hidayat Ullah Khan. "The Physical Significance of Time Conformal Minkowski Spacetime." April 2020 39, no. 2 (2020): 365–70. http://dx.doi.org/10.22581/muet1982.2002.12.

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The Minkowsiki spacetime is flat and there is no source of gravitation. The time conformal factor is adding some cuvature to this spacetime which introduces some source of gravitation to the spacetime. For the Minkowski spacetime the Einstein Field equation tells nothing, because all the components of the Ricci curvature tensor are zero, but for the time conformal Minkowski spacetime some of them are non zero. Calculating the components of the Ricci tensor and using the Einstein field equations, expressions for the cosmological constant are cacultaed. These expressions give some information for the cosmological constant. Generally, the Noether symmetry generator corresponding to the energy content in the spacetime disapeares by introducing the time conformal factor, but our investigations in this paper reveals that it appears somewhere with some re-scale factor. The appearance of the time like isometry along with some re-scaling factor will rescale the energy content in the corresponding particular time conformal Minkowski spacetime. A time conformal factor of the form () is introduced in the Minkowski spacetime for the invistigation of the cosmological constant. The Noether symmetry equation is used for the Lagrangian of general time conformal Minkowski spacetime to find all those particular Minkowski spacetimes that admit the time conformal factor. Besides the Noether symmetries the cosmology constant is calculated in the corresponding spacetimes.

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Shaikh, Absos Ali, Sudhir Kumar Srivastava, and Dhyanesh Chakraborty. "Curvature properties of anisotropic scale invariant metrics." International Journal of Geometric Methods in Modern Physics 16, no. 06 (2019): 1950086. http://dx.doi.org/10.1142/s0219887819500865.

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The objective of this paper is to study the curvature restricted geometric properties of anisotropic nonrelativistic scale invariant metrics, namely, Lifshitz and Schrödinger spacetime metrics. It is found that the Lifshitz spacetime metric admits two important pseudosymmetric type curvature conditions [Formula: see text] and [Formula: see text]. Also, it is [Formula: see text]-quasi Einstein and generalized Roter type manifold. Finally, Lifshitz spacetime is compared with Schrödinger spacetime.

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Kunkler, Michael. "Reframing the general theory of relativity." Physics Essays 35, no. 3 (2022): 276–86. http://dx.doi.org/10.4006/0836-1398-35.3.276.

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The general theory of relativity extends the special theory of relativity to account for gravity (acceleration) and results in the postulation that matter curves spacetime, where gravitation is the embodiment of the spacetime curvature. The curvature of spacetime is modeled using Riemannian geometry. In this paper, it is proposed that matter rotates spacetime hyperbolically, rather than curves spacetime. As a result, gravitation is the embodiment of the hyperbolic rotation of spacetime. Regions in spacetime that have a larger magnitude of rotation relative to other regions of spacetime, ceteris paribus, experience stronger gravity, gravitational time dilation, gravitational length contraction, and gravitational frequency shift toward the red (blue) in the electromagnetic waves moving away (toward).

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Singh, Parampreet. "Is classical flat Kasner spacetime flat in quantum gravity?" International Journal of Modern Physics D 25, no. 08 (2016): 1642001. http://dx.doi.org/10.1142/s0218271816420013.

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Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology (LQC). We find that even though the spacetime curvature vanishes at the classical level, nontrivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces nonvanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The noncurvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with nontrivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.

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Delaporte, Héloïse, and Astrid Eichhorn. "The principled-parameterized approach to gravitational collapse." Journal of Cosmology and Astroparticle Physics 2025, no. 03 (2025): 074. https://doi.org/10.1088/1475-7516/2025/03/074.

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Abstract New physics beyond General Relativity impacts black-hole spacetimes. The effects of new physics can be investigated in a largely theory-agnostic way by following the principled-parameterized approach. In this approach, a classical black-hole metric is upgraded by following a set of principles, such as regularity, i.e., the absence of curvature singularities. We expect these principles to hold in many theories beyond General Relativity. In the present paper, we implement this approach for time-dependent spacetimes describing gravitational collapse. We find that the Vaidya spacetime becomes regular through the same modification of the spacetime metric as stationary black-hole spacetimes [1–3]. We investigate null geodesics and find indications that the modification is even sufficient to render null geodesics future complete. Finally, we find that the modification of the spacetime structure results in violations of the null energy condition in a finite region inside the apparent horizon of the black hole that forms. Null geodesics are attracted to the boundary of this region, such that the new-physics effects are shielded from asymptotic observers. An exception occurs, if the classical spacetime has a naked singularity. Then, the upgraded spacetime is singularity-free and null geodesics from the regular core can escape towards asymptotic observers.

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Suh, Young, Vasant Chavan, and Naeem Pundeer. "Pseudo-quasi-conformal curvature tensor and spacetimes of general relativity." Filomat 35, no. 2 (2021): 657–66. http://dx.doi.org/10.2298/fil2102657s.

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In the present paper, we carried out a systematic investigation of pseudo-quasi-conformal curvature tensor has been made on the four-dimensional spacetime of general relativity. The spacetime fulfilling Einstein?s field equations with vanishing of pseudo-quasi-conformal curvature tensor is being considered and existence of Killing and conformal Killing vectors on such spacetime have been established. At last, we extend the similar case for the investigation of cosmological models with dust and perfect fluid spacetime.

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Creighton, Teviet, Fredrick A. Jenet, and Richard H. Price. "PULSAR TIMING AND SPACETIME CURVATURE." Astrophysical Journal 693, no. 2 (2009): 1113–17. http://dx.doi.org/10.1088/0004-637x/693/2/1113.

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Hestenes, David. "Curvature calculations with spacetime algebra." International Journal of Theoretical Physics 25, no. 6 (1986): 581–88. http://dx.doi.org/10.1007/bf00670472.

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Terashima, Hiroaki, and Masahito Ueda. "Spin decoherence by spacetime curvature." Journal of Physics A: Mathematical and General 38, no. 9 (2005): 2029–37. http://dx.doi.org/10.1088/0305-4470/38/9/013.

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Bernar, Rafael P., Luís C. B. Crispino, and Atsushi Higuchi. "Circular geodesic radiation in Schwarzschild spacetime: A semiclassical approach." International Journal of Modern Physics D 27, no. 11 (2018): 1843002. http://dx.doi.org/10.1142/s0218271818430022.

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Extreme curvature settings and nontrivial causal structure of curved spacetimes may have interesting theoretical and practical implications for quantum field theories. Radiation emission in black hole spacetimes is one such scenario in which the semiclassical approach, i.e. quantum fields propagating in a nondynamical background spacetime, adds a very simple conceptual point of view and allows us to compute the emitted power in a straightforward way. Within this context, we reexamine sources in circular orbit around a Schwarzschild black hole, investigating the emission of scalar, electromagnetic and gravitational radiations. The analysis of the differences and similarities between these cases provide an excellent overview of the powerful conceptual and computational tool that is quantum field theory in curved spacetime.

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Ali, Mohabbat, Mohd Vasiulla, and Meraj Ali Khan. "Geometric and Physical Characteristics of Pseudo-Schouten Symmetric Manifolds." Axioms 14, no. 4 (2025): 256. https://doi.org/10.3390/axioms14040256.

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In this paper, we introduce and study the properties of pseudo-Schouten symmetric manifolds (PSS)n. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes within the framework of general relativity. Furthermore, we investigate their role in relativistic spacetime models by considering Einstein’s field equations with and without a cosmological constant. We also show that pseudo-Schouten symmetric spacetimes satisfying Einstein’s equations with a quadratic Killing energy–momentum tensor or a Codazzi-type energy–momentum tensor cannot have non-zero constant scalar curvature. Finally, the existence of pseudo-Schouten symmetric spacetime is shown by constructing an explicit non-trivial example.

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SHAIKH, ABSOS ALI, TRAN QUOC BINH, and HARADHAN KUNDU. "Curvature Properties of Generalized pp-Wave Metrics." Kragujevac Journal of Mathematics 45, no. 02 (2021): 237–58. http://dx.doi.org/10.46793/kgjmat2102.237s.

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The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisﬁes the pseudosymmetric type condition P ⋅ P = −13Q(S,P). Again we investigate the suﬃcient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent. Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. Again the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally, we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

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Demir, Durmuş Ali. "Curvature-Restored Gauge Invariance and Ultraviolet Naturalness." Advances in High Energy Physics 2016 (2016): 1–4. http://dx.doi.org/10.1155/2016/6727805.

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It is shown that (aΛ2+b|H|2)R in a spacetime of curvature R is a natural ultraviolet (UV) completion of (aΛ4+bΛ2|H|2) in the flat-spacetime Standard Model (SM) with Higgs field H, UV scale Λ, and loop factors a and b. This curvature completion rests on the fact that Λ-mass gauge theory in flat spacetime turns, on the cut view R=4Λ2, into a massless gauge theory in curved spacetime. It provides a symmetry reason for curved spacetime, wherein gravity and matter are both low-energy effective phenomena. Gravity arises correctly if new physics exists with at least 63 more bosons than fermions, with no need to interact with the SM and with dark matter as a natural harbinger. It can source various cosmological, astrophysical, and collider phenomena depending on its spectrum and couplings to the SM.

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Coley, A. A., and S. Hervik. "Universality and Constant Scalar Curvature Invariants." ISRN Geometry 2011 (September 6, 2011): 1–9. http://dx.doi.org/10.5402/2011/248615.

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A classical solution is called universal if the quantum correction is a multiple of the metric. Therefore, universal solutions play an important role in the quantum theory. We show that in a spacetime which is universal all scalar curvature invariants are constant (i.e., the spacetime is CSI).

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ALÍAS, LUIS J., and A. GERVASIO COLARES. "Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 3 (2007): 703–29. http://dx.doi.org/10.1017/s0305004107000576.

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AbstractIn this paper we study the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker (GRW) spacetimes. In particular, we consider the following question: under what conditions must a compact spacelike hypersurface with constant higher order mean curvature in a spatially closed GRW spacetime be a spacelike slice? We prove that this happens, essentially, under the so callednull convergence condition. Our approach is based on the use of the Newton transformations (and their associated differential operators) and the Minkowski formulae for spacelike hypersurfaces.

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De, Uday, Young Suh, Sudhakar Chaubey, and Sameh Shenawy. "On pseudo H-symmetric Lorentzian manifolds with applications to relativity." Filomat 34, no. 10 (2020): 3287–97. http://dx.doi.org/10.2298/fil2010287d.

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In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-symmetric manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian manifolds. Also, we provide several interesting results. Among others, we prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar curvature of the manifold vanishes and conversely. Moreover, we deal with pseudo H-symmetric perfect fluid spacetimes and obtain several interesting results. Also, we present some results of the spacetime satisfying divergence free H-curvature tensor. Finally, we construct a non-trivial Lorentzian metric of (PHS)4.

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Chattopadhyay, Kaushik, Arindam Bhattacharyya, and Dipankar K. Debnath. "A Study of Spacetimes with vanishing M−projective Curvature Tensor." Journal of the Tensor Society 12, no. 01 (2007): 23–31. http://dx.doi.org/10.56424/jts.v12i01.10594.

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In this paper we study about the M−projectively flat perfect fluid spacetime. First of all we showed that the Riemannian curvature tensor of an M−projectively flat spacetime is covariantly constant. Then we found the length of the Ricci operator in an M−projectively flat perfect fluid spacetime and proved that the isotropic pressure and entry density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant are constant. Then we showed that an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant and obeying the timelike convergence condition has positive isotropic pressure. Further we showed that the isotropic pressure and the energy density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant vanishes in a purely electromagnetic distribution. Lastly we showed that an M−projectively flat perfect fluid spacetime with the energy momentum tensor of an electromagnetic field such that the spacetimesatisfies Einsteins field equation without cosmological constant is a Euclidean space

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Shaikh, Absos, A. AhmedFaizuddin, Biswa Datta, and Mousumi Sarkar. "On geometric properties of topologically charged Ellis-Bronnikov-type wormhole spacetime." Filomat 38, no. 15 (2024): 5527–41. https://doi.org/10.2298/fil2415527s.

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In this paper, we have studied the geometric properties of topologically charged Ellis-Bronnikov-type wormhole (briefly, TCEBW) spacetime. The TCEBW spacetime is a static and spherically symmetric solution of the Einstein field equations with a non-zero cosmological constant. We obtained several im-portant geometric properties viz. pseudosymmetry due to conformal curvature as well as conharmonic curvature, Ricci generalized pseudosymmetry and Ricci generalized projectively pseudosymmetry. Also, it is shown that the TCEBW spacetime is generalized Roter type, 2-quasi-Einstein, Einstein manifold of level 3 and its conformal 2-forms are recurrent. As a special case, the geometric properties of Morris-Thorne wormhole spacetime are analyzed. Also, we have shown that the TCEBW spacetime admits an almost ?-Ricci-Yamabe soliton and an almost ?-Ricci soliton. Finally, a comparison between Morris-Thorne wormhole and TCEBW spacetime regarding their geometric structures is exhibited.

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Amelino-Camelia, Giovanni, Leonardo Barcaroli, Stefano Bianco, and Laura Pensato. "Planck-Scale Dual-Curvature Lensing and Spacetime Noncommutativity." Advances in High Energy Physics 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/6075920.

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It was recently realized that Planck-scale momentum-space curvature, which is expected in some approaches to the quantum-gravity problem, can produce dual-curvature lensing, a feature which mainly affects the direction of observation of particles emitted by very distant sources. Several gray areas remain in our understanding of dual-curvature lensing, including the possibility that it might be just a coordinate artifact and the possibility that it might be in some sense a by-product of the better studied dual-curvature redshift. We stress that data reported by the IceCube neutrino telescope should motivate a more vigorous effort of investigation of dual-curvature lensing, and we observe that studies of the recently proposed “ρ-Minkowski noncommutative spacetime” could be valuable from this perspective. Through a dedicated ρ-Minkowski analysis, we show that dual-curvature lensing is not merely a coordinate artifact and that it can be present even in theories without dual-curvature redshift.

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SAHARIAN, A. A. "CASIMIR EFFECT IN DE SITTER SPACETIME." International Journal of Modern Physics: Conference Series 03 (January 2011): 215–26. http://dx.doi.org/10.1142/s2010194511001309.

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The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch–Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

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Gallerati, Antonio. "Negative-curvature spacetime solutions for graphene." Journal of Physics: Condensed Matter 33, no. 13 (2021): 135501. http://dx.doi.org/10.1088/1361-648x/abd9a2.

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Choudhury, Sayantan, Joydip Mitra, and Soumitra SenGupta. "Fermion localization in higher curvature spacetime." Classical and Quantum Gravity 35, no. 2 (2017): 025007. http://dx.doi.org/10.1088/1361-6382/aa91f7.

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Babul, Arif, Tsvi Piran, and David N. Spergel. "Superconducting cosmic strings. II. Spacetime curvature." Physics Letters B 209, no. 4 (1988): 477–84. http://dx.doi.org/10.1016/0370-2693(88)91177-x.

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Janis, Allen I. "On Mass, Spacetime Curvature, and Gravity." Physics Teacher 56, no. 1 (2018): 12–13. http://dx.doi.org/10.1119/1.5018679.

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