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Journal articles on the topic 'Spacetime curvature'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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1

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-mom
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2

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 determ
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3

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
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4

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 inv
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6

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-existenc
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7

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 i
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8

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 manifol
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9

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
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10

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 inheri
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11

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 se
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12

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 v
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13

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
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14

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 responsib
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15

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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16

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 invarian
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17

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
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18

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 gener
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19

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 ene
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20

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 w
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21

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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22

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 s
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23

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 vecto
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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 [Formul
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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
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26

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
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27

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 fo
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28

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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29

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, ceteri
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30

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 Kasne
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31

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 bec
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32

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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33

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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34

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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35

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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36

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, electromagne
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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
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38

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 sp
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39

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
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40

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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41

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 Minkows
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42

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
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43

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
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44

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
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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 sh
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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 de
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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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48

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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49

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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50

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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