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Journal articles on the topic 'Higher dimensional General Relativity'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Reddy, D. R. K., and R. L. Naidu. "A Higher Dimensional Inflationary Universe in General Relativity." International Journal of Theoretical Physics 47, no. 9 (February 6, 2008): 2339–43. http://dx.doi.org/10.1007/s10773-008-9667-4.

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2

Rahaman, F., Saibal Ray, M. Kalam, and M. Sarker. "Do Solar System Tests Permit Higher Dimensional General Relativity?" International Journal of Theoretical Physics 48, no. 11 (August 18, 2009): 3124–38. http://dx.doi.org/10.1007/s10773-009-0110-2.

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3

WITEK, HELVI. "NUMERICAL RELATIVITY IN HIGHER-DIMENSIONAL SPACE–TIMES." International Journal of Modern Physics A 28, no. 22n23 (September 20, 2013): 1340017. http://dx.doi.org/10.1142/s0217751x13400174.

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Black holes are among the most exciting phenomena predicted by General Relativity and play a key role in fundamental physics. Many interesting phenomena involve dynamical black hole configurations in the high curvature regime of gravity. In these lecture notes I will summarize the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic D-dimensional space–times. The present notes are based on my lectures given at the NR/HEP2 spring school at IST/Lisbon (Portugal) from March 11–14, 2013.

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4

Chiba, T. "Cylindrical Dust Collapse in General Relativity: Toward Higher Dimensional Collapse." Progress of Theoretical Physics 95, no. 2 (February 1, 1996): 321–38. http://dx.doi.org/10.1143/ptp.95.321.

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5

Ishibashi, Akihiro. "Symmetry Properties of Black Holes in Higher Dimensional General Relativity." Progress of Theoretical Physics Supplement 172 (2008): 202–9. http://dx.doi.org/10.1143/ptps.172.202.

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6

Kandalkar, S. P., and S. P. Gawande. "Anisotropic fluid distribution in higher dimensional general theory of relativity." Astrophysics and Space Science 315, no. 1-4 (April 26, 2008): 87–91. http://dx.doi.org/10.1007/s10509-008-9800-0.

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7

REALL, HARVEY S. "HIGHER DIMENSIONAL BLACK HOLES." International Journal of Modern Physics D 21, no. 12 (November 2012): 1230001. http://dx.doi.org/10.1142/s0218271812300017.

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8

MONTE, EDMUNDO M. "EMBEDDING VERSUS IMMERSION IN GENERAL RELATIVITY." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1501–4. http://dx.doi.org/10.1142/s0217751x09044887.

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We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory, since the causal structure of the immersed space-time is not preserved by the immersion.

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9

Aygün, M., S. Aygün, I. Yilmaz, H. Baysal, and I. Tarhan. "Møller Energy–Momentum Complex in General Relativity for Higher Dimensional Universes." Chinese Physics Letters 24, no. 7 (June 28, 2007): 1821–24. http://dx.doi.org/10.1088/0256-307x/24/7/010.

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10

Ashtekar, Abhay, and David Sloan. "Action and Hamiltonians in higher-dimensional general relativity: first-order framework." Classical and Quantum Gravity 25, no. 22 (November 3, 2008): 225025. http://dx.doi.org/10.1088/0264-9381/25/22/225025.

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11

KATORE, S. D., K. S. ADHAV, V. G. METE, and A. Y. SHAIKH. "A higher-dimensional Bianchi type-I inflationary Universe in general relativity." Pramana 78, no. 1 (December 24, 2011): 101–7. http://dx.doi.org/10.1007/s12043-011-0208-y.

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12

Nashed, Gamal G. L. "Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity." Chinese Physics B 22, no. 2 (February 2013): 020401. http://dx.doi.org/10.1088/1674-1056/22/2/020401.

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13

BAYSAL, HÜSNÜ. "MØLLER ENERGY–MOMENTUM COMPLEX FOR HIGHER-DIMENSIONAL SPHERICALLY SYMMETRIC SPACETIME IN GENERAL RELATIVITY." Modern Physics Letters A 27, no. 40 (December 19, 2012): 1250231. http://dx.doi.org/10.1142/s0217732312502318.

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We have calculated the total energy–momentum distribution associated with (n+2)-dimensional spherically symmetric model of the universe by using the Møller energy–momentum definition in general relativity (GR). We have found that components of Møller energy and momentum tensor for given spacetimes are different from zero. Also, we are able to get energy and momentum density of various well-known wormholes and black hole models by using the (n+2)-dimensional spherically symmetric metric. Also, our results have been discussed and compared with the results for four-dimensional spacetimes in literature.

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14

Khadekar, G. S., and Rupali Wanjari. "Geometry of Quark and Strange Quark Matter in Higher Dimensional General Relativity." International Journal of Theoretical Physics 51, no. 5 (November 16, 2011): 1408–15. http://dx.doi.org/10.1007/s10773-011-1016-3.

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15

WESSON, PAUL S., SANJEEV S. SEAHRA, and HONGYA LIU. "A FORMAL APPROACH TO MACHIAN GENERAL RELATIVITY." International Journal of Modern Physics D 11, no. 09 (October 2002): 1347–54. http://dx.doi.org/10.1142/s0218271802002669.

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We take Mach's principle to mean that the local properties of a test particle should depend on the global properties of the geometry. Using a complex wave-like metric and an appropriate redefinition of the energy-momentum tensor, we show this to be possible in principle within the context of general relativity. We outline implications for higher-dimensional theories of gravity.

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16

Grunau, Saskia, and Jutta Kunz. "Hyperelliptic Functions and Motion in General Relativity." Mathematics 10, no. 12 (June 7, 2022): 1958. http://dx.doi.org/10.3390/math10121958.

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Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with a set of examples of genus g=2: higher dimensional Schwarzschild black holes, rotating dyonic U(1)2 black holes, and black rings.

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17

Camanho, Xián O., José D. Edelstein, and Alexander Zhiboedov. "Weakly coupled gravity beyond general relativity." International Journal of Modern Physics D 24, no. 12 (October 2015): 1544031. http://dx.doi.org/10.1142/s0218271815440319.

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We explore four-dimensional (4D) weakly coupled gravity beyond general relativity in an on-shell language, focusing on the graviton three-point vertex. This admits a novel structure which can be attributed to a term cubic in the Riemann tensor. We consider a generalization of the Shapiro time delay experiment that involves polarized gravitons and show that the new vertex leads to causality violation. Fixing the problem demands the inclusion of an infinite tower of massive higher spin states. Perturbative string theory provides an example of this phenomenon, the only known so far. Interestingly enough, the same argument being applied to inflation suggests that stringy signatures may be hidden in the non-Gaussianities of the primordial gravity wave spectrum.

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18

Anderson, Edward, and Reza Tavakol. "Geodesics, the equivalence principle and singularities in higher-dimensional general relativity and braneworlds." Journal of Cosmology and Astroparticle Physics 2005, no. 10 (October 28, 2005): 017. http://dx.doi.org/10.1088/1475-7516/2005/10/017.

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19

Mete, V. G., V. M. Umarkar, and A. M. Pund. "Higher Dimensional Plane Symmetric Cosmological Models with Two-Fluid Source in General Relativity." International Journal of Theoretical Physics 52, no. 12 (August 10, 2013): 4439–44. http://dx.doi.org/10.1007/s10773-013-1763-4.

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20

Krori, K. D., P. Borgohain, and Kanika Das. "Exact interior solutions in higher dimensions." Canadian Journal of Physics 67, no. 1 (January 1, 1989): 25–30. http://dx.doi.org/10.1139/p89-002.

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21

ANEZIRIS, C., A. P. BALACHANDRAN, M. BOURDEAU, S. JO, T. R. RAMADAS, and R. D. SORKIN. "STATISTICS AND GENERAL RELATIVITY." Modern Physics Letters A 04, no. 04 (February 1989): 331–38. http://dx.doi.org/10.1142/s021773238900040x.

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There exists a class of particle-like topological excitations in generally covariant theories called geons, discussed by Friedman and Sorkin, and by these authors, and others. Here, we show by specific examples that certain of these geons can be so quantized that they are characterized by no definite statistics. For instance, three-dimensional geons may be neither bosons nor fermions (nor paraparticles). It can also happen, as pointed out before by Sorkin, and as we briefly discuss here, that a tensorial (spinorial) goen obeys Fermi (Bose) statistics. Our usual conceptions about the statistics of particle species thus do not seem to be valid in generally covariant theories, at least without further physical inputs such as, perhaps, the possibility of topology change.

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22

Bejancu, Aurel. "On Higher Dimensional Kaluza-Klein Theories." Advances in High Energy Physics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/148417.

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We present a new method for the study of general higher dimensional Kaluza-Klein theories. Our new approach is based on the Riemannian adapted connection and on a theory of adapted tensor fields in the ambient space. We obtain, in a covariant form, the fully general 4D equations of motion in a (4 +n)D general gauge Kaluza-Klein space. This enables us to classify the geodesics of the (4 +n)D space and to show that the induced motions in the 4D space bring more information than motions from both the 4D general relativity and the 4D Lorentz force equations. Finally, we note that all the previous studies on higher dimensional Kaluza-Klein theories are particular cases of the general case considered in the present paper.

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23

Concha, P. K., D. M. Peñafiel, E. K. Rodríguez, and P. Salgado. "Even-dimensional General Relativity from Born–Infeld gravity." Physics Letters B 725, no. 4-5 (October 2013): 419–24. http://dx.doi.org/10.1016/j.physletb.2013.07.019.

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24

Khadekar, G. S., and P. D. Shobhane. "Higher dimensional exact solutions for a charged fluid sphere in general theory of relativity." Astrophysics and Space Science 315, no. 1-4 (June 2008): 307–17. http://dx.doi.org/10.1007/s10509-008-9833-4.

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25

YILMAZ, IHSAN, and ATTILA ALTAY YAVUZ. "HIGHER-DIMENSIONAL COSMOLOGICAL MODELS WITH STRANGE QUARK MATTER." International Journal of Modern Physics D 15, no. 04 (April 2006): 477–83. http://dx.doi.org/10.1142/s0218271806008267.

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In this article, we study higher-dimensional cosmological models with quark–gluon plasma in the context of general relativity. For this purpose, we consider quark–gluon plasma as a perfect fluid in the higher-dimensional universes. After solving Einstein's field equations, we have analyzed this matter for the different types of universes in the higher- and four-dimensional universes. Also, we have discussed the features of obtained solutions.

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26

HARTLE, J. B. "GENERAL RELATIVITY AND QUANTUM MECHANICS." International Journal of Modern Physics A 16, no. 01 (January 10, 2001): 1–16. http://dx.doi.org/10.1142/s0217751x01002993.

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Usual quantum mechanics requires a fixed background spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically.

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27

Thuan, Vo Van, and Nguyen Thi Kim Thoa. "The Modern Induced Matter Approach of General Relativity for Quantum Mechanics." Communications in Physics 26, no. 3 (February 8, 2017): 209. http://dx.doi.org/10.15625/0868-3166/26/3/8956.

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Wesson and his co-workers developed so-called space-time-matter theory (5D-STM) as a generalization of Kaluza-Klein theory, where the extra-dimension in the 5D space-time is no more compacted, but keeping extended in a macroscopic scale to describe the properties of matter in 4D physics. In a trend of 5D-STM approach (or the induced-matter theory), following a bi-cylindrical model of geometrical dynamics, a recent study has shown that the higher 6D-dimensional gravitational equation leads to bi-geodesic description in an extended timespace symmetry which ﬁts Hubble expansion in a ”microscopic” cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory.

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28

Priyokumar, Singh K., and Baro Jiten. "Higher Dimensional LRS Bianchi Type-I String Cosmological Model with Bulk Viscosity in General Relativity." Indian Journal of Science and Technology 14, no. 16 (April 30, 2021): 1239–49. http://dx.doi.org/10.17485/ijst/v14i16.240.

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29

Trofimenko, A. P., and V. S. Gurin. "White and Grey Holes in Higher-Dimensional Representation of Extended Space-Time Manifolds of General Relativity." Annalen der Physik 503, no. 4 (1991): 295–303. http://dx.doi.org/10.1002/andp.19915030407.

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30

Blagojević, M., and B. Cvetković. "Entropy in three-dimensional general relativity: Kerr-AdS black hole." Physics Letters B 801 (February 2020): 135180. http://dx.doi.org/10.1016/j.physletb.2019.135180.

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31

SAHOO, Pradyumn Kumar, and Bivudutta MISHRA. "Higher-dimensional Bianchi type-III universe with strange quark matter attached to string cloud in general relativity." TURKISH JOURNAL OF PHYSICS 39 (2015): 43–53. http://dx.doi.org/10.3906/fiz-1403-5.

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32

WESSON, PAUL S. "THE EQUIVALENCE PRINCIPLE AS A PROBE FOR HIGHER DIMENSIONS." International Journal of Modern Physics D 14, no. 12 (December 2005): 2315–18. http://dx.doi.org/10.1142/s0218271805007991.

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Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical symmetry which can be broken, perhaps at a level detectable by new tests in space.

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33

SALISBURY, DONALD. "GAUGE FIXING AND OBSERVABLES IN GENERAL RELATIVITY." Modern Physics Letters A 18, no. 33n35 (November 20, 2003): 2475–82. http://dx.doi.org/10.1142/s0217732303012714.

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The conventional group of four-dimensional diffeomorphisms is not realizeable as a canonical transformation group in phase space. Yet there is a larger field-dependent symmetry transformation group which does faithfully reproduce 4-D diffeomorphism symmetries. Some properties of this group were first explored by Bergmann and Komar. More recently the group has been analyzed from the perspective of projectability under the Legendre map. Time translation is not a realizeable symmetry, and is therefore distinct from diffeomorphism-induced symmetries. This issue is explored further in this paper. It is shown that time is not "frozen". Indeed, time-like diffeomorphism invariants must be time-dependent. Intrinsic coordinates of the type proposed by Bergmann and Komar are used to construct invariants. Lapse and shift variables are retained as canonical variables in this approach, and therefore will be subject to quantum fluctuations in an eventual quantum theory. Concepts and constructions are illustrated using the relativistic classical and quantum free particle. In this example concrete time-dependent invariants are displayed and fluctuation in proper time is manifest.

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34

BEESHAM, A. "HIGHER DIMENSIONAL INHOMOGENEOUS DUST COLLAPSE AND COSMIC CENSORSHIP." International Journal of Modern Physics A 17, no. 20 (August 10, 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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35

Langley, Rob. "Quantum Gravity as Higher Dimensional Perspective." Applied Physics Research 8, no. 4 (July 29, 2016): 38. http://dx.doi.org/10.5539/apr.v8n4p38.

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Although highly predictive in their respective macroscopic and microscopic domains of applicability, General Relativity and quantum mechanics are mathematically incompatible, perhaps most markedly in assumptions in their formalisms concerning the nature of space and time. In <em>perspective</em> we already have a conceptual structure that links the local, macroscopic frame and the remote, apparently microscopic frame. A mathematical principle is invoked as a natural limit on D(n), so that effects which are clearly perspectival at D=3 become ‘more real’ (<em>effectively</em> observer-independent) with each D(n) increment. For instance, the apparently microscopic becomes the effectively microscopic and <em>scale extremes are juxtaposed</em>, so that black holes are local, macroscopic vanishing-points, in a similar way to that in which in projective geometry the point at infinity is incorporated into the foreground. (In other words, <em>a black hole is a blown-up ‘Planck-scale’ singularity</em>.) Characteristics of the earthbound frame are applied to D>3, suggesting a physical basis for entanglement, and perspectival interpretations of quantum gravity, dimensional reduction and the information paradox. We claim that the familiar processes whereby multiple physical states become describable by a single state in which composition information appears to be lost (e.g., ‘falling into a black hole’, the state of quantum linearity, and the state of freefall) are all examples of effective convergence of a space or <em>n</em>-surface to a single point of perspective.

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36

Chakraborty, Sumanta. "Bound on Photon Circular Orbits in General Relativity and Beyond." Galaxies 9, no. 4 (November 7, 2021): 96. http://dx.doi.org/10.3390/galaxies9040096.

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The existence of a photon circular orbit can tell us a lot about the nature of the underlying spacetime, since it plays a pivotal role in the understanding of the characteristic signatures of compact objects, namely the quasi-normal modes and shadow radius. For this purpose, determination of the location of the photon circular orbit is of utmost importance. In this work, we derive bounds on the location of the photon circular orbit around compact objects within the purview of general relativity and beyond. As we have explicitly demonstrated, contrary to the earlier results in the context of general relativity, the bound on the location of the photon circular orbit is not necessarily an upper bound. Depending on the matter content, it is possible to arrive at a lower bound as well. This has interesting implications for the quasi-normal modes and shadow radius, the two key observables related to the strong field tests of gravity. Besides discussing the bound for higher dimensional general relativity, we have also considered how the bound on the photon circular orbits gets modified in the braneworld scenario, for pure Lovelock and general Lovelock theories of gravity. Implications of these results for compact objects were also discussed.

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37

PELEG, YOAV. "INTERACTING THIRD QUANTIZED GENERAL RELATIVITY AND CHANGE OF TOPOLOGY." Modern Physics Letters A 08, no. 20 (June 28, 1993): 1849–58. http://dx.doi.org/10.1142/s0217732393001574.

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The Wheeler-DeWitt equation can be treated as a dynamical equation of a field theory on superspace, which is a free Klein-Gordon field (in an infinite-dimensional curved space) with a non-positive-definite mass squared term. This suggests that one should add an interaction term to the third quantized theory, and by that to get a Hamiltonian which is bounded from below. This process may allow a change of topology. A consistent third quantized theory can be defined in a subspace of superspace for which the Ricci scalar is zero. We consider a simple example of such subspace, and examine (in it) two kinds of interactions, one which is local in superspace and one which is local in the physical space.

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38

Han, Yu, Yongge Ma, and Xiangdong Zhang. "Connection dynamics of higher-dimensional scalar–tensor theories of gravity." Modern Physics Letters A 29, no. 28 (September 14, 2014): 1450134. http://dx.doi.org/10.1142/s021773231450134x.

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The scalar–tensor theories (STTs) of gravity in spacetime dimensions (D+1)>2 are studied. By performing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter ω. The Hamiltonian structures in both sectors are similar to the corresponding structures of four-dimensional cases. It turns out that, similar to the case of general relativity (GR), there is also a symplectic reduction from the canonical structure of so (D+1) Yang–Mills theories coupled to the scalar field to the canonical structure of the geometrical STTs. Therefore, the non-perturbative loop quantum (LQG) gravity techniques can also be applied to the STTs in D+1 dimensions based on their connection-dynamical formalism.

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39

Ray, Saibal, Rikpratik Sengupta, and Himanshu Nimesh. "Gravastar: An alternative to black hole." International Journal of Modern Physics D 29, no. 05 (March 25, 2020): 2030004. http://dx.doi.org/10.1142/s0218271820300049.

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In this work, we review thoroughly the origin, development and present status of gravastar which has been thought to be an alternative to black hole along with its future feasibility in the sense of astrophysical observation. The Mazur–Mottola model of the gravastar is introduced first followed by a review of its generalizations within the context of general relativity including physical applications like primordial and cylindrical gravastars. The study of gravastar in higher- and lower-dimensional general relativity (GR) including the higher-dimensional theories with physical insight like the Randall–Sundrum model is presented. The gravastar models in a number of modified gravity models starting from [Formula: see text] to Rastall–Rainbow gravity have been reviewed.

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40

Bajardi, Francesco, Konstantinos F. Dialektopoulos, and Salvatore Capozziello. "Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity." Symmetry 12, no. 3 (March 2, 2020): 372. http://dx.doi.org/10.3390/sym12030372.

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We study a theory of gravity of the form f ( G ) where G is the Gauss–Bonnet topological invariant without considering the standard Einstein–Hilbert term as common in the literature, in arbitrary ( d + 1 ) dimensions. The approach is motivated by the fact that, in particular conditions, the Ricci curvature scalar can be easily recovered and then a pure f ( G ) gravity can be considered a further generalization of General Relativity like f ( R ) gravity. Searching for Noether symmetries, we specify the functional forms invariant under point transformations in a static and spherically symmetric spacetime and, with the help of these symmetries, we find exact solutions showing that Gauss–Bonnet gravity is significant without assuming the Ricci scalar in the action.

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41

Ita, Eyo Eyo. "4-dimensional General Relativity from the instrinsic spatial geometry of Yang–Mills theory." Nuclear Physics B 852, no. 3 (November 2011): 681–95. http://dx.doi.org/10.1016/j.nuclphysb.2011.07.004.

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42

Barrow, John D. "Maximum force and naked singularities in higher dimensions." International Journal of Modern Physics D 29, no. 14 (August 20, 2020): 2043008. http://dx.doi.org/10.1142/s0218271820430087.

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We discuss the existence of maximum forces in ([Formula: see text])-dimensional spacetimes and show that the existence of a mass-independent maximum force does not occur in general relativity in spaces of more than three dimensions. Instead, the maximum force increases with the masses of merging objects as [Formula: see text] and allows unbounded gravitational forces to occur. This suggests that naked singularities can arise in more than three dimensions because they are unprotected by a maximum force at the horizon surface. This creates a new perspective on the expectation of naked singularities in higher dimensions.

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43

SASAKURA, NAOKI. "THE LOWEST MODES AROUND GAUSSIAN SOLUTIONS OF TENSOR MODELS AND THE GENERAL RELATIVITY." International Journal of Modern Physics A 23, no. 24 (September 30, 2008): 3863–90. http://dx.doi.org/10.1142/s0217751x0804130x.

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In the paper arXiv:0706.1618[hep-th], the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-3 tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R2-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.

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44

Overduin, James, Nathan Prins, and Joohan Lee. "Supernova constraints on higher-dimensional cosmology with a phantom field." International Journal of Modern Physics D 25, no. 06 (May 2016): 1650069. http://dx.doi.org/10.1142/s0218271816500693.

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We use observational data on the magnitude-redshift relation for Type Ia supernovae (SNeIa) together with constraints on the ages of the oldest stars to rule out a higher-dimensional extension of General Relativity with a negative kinetic energy scalar field. This theory is of considerable physical interest because it produces accelerated expansion at both early and late times with a single new field, as in quintessential inflation scenarios. It is also of mathematical interest because it is characterized by an analytic expression for the macroscopic scale factor [Formula: see text]. We show that cosmological solutions of this theory can be usefully parametrized by a single quantity, the lookback time [Formula: see text] corresponding to the transition from deceleration to acceleration. Supernovae data from the recently released Supernova Cosmology Project (SCP) Union 2.1 compilation single out a narrow range of values for [Formula: see text]. In the context of the theory, however, these same values of [Formula: see text] imply that the universe is much older than the oldest observed stars.

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Wesson, Paul S. "Comments on the Cosmological Constant Problem and How it Can be Solved." International Journal of Modern Physics D 06, no. 05 (October 1997): 643–48. http://dx.doi.org/10.1142/s021827189700039x.

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The problem of disparate estimates of the energy density of the vacuum can be solved, at least in principle, by reducing a higher-dimensional theory of gravity to general relativity and a local cosmological "constant."

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Lalremruati, P. C., and Sanjeev Kalita. "Is It Possible to See the Breaking Point of General Relativity near the Galactic Center Black Hole? Consideration of Scalaron and Higher-dimensional Gravity." Astrophysical Journal 925, no. 2 (February 1, 2022): 126. http://dx.doi.org/10.3847/1538-4357/ac3af0.

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Abstract The Galactic center black hole is a putative laboratory to test general relativity (GR) and constrain its alternatives. f(R) scalaron gravity is an interesting alternative to GR and has tremendous prospects for astrophysics and fundamental physics near the black hole. In this work, we search for breaking points of GR through estimation of pericenter shift of stellar orbits with semimajor axis a = (45–1000) au. The black hole spin is taken as the maximum χ = 0.99, and orbital eccentricity is taken as e = 0.9. We work with theoretical scalaron field amplitude and coupling, predicted by Kalita, and also consider the constraints reported by Hees et al. The scalaron mass is taken in the range (10−22–10−17) eV. It is found that GR suppresses scalaron gravity at all orbital radii for the theoretical values of scalaron field coupling predicted by Kalita. Breaking point arises only for higher scalaron coupling resulting from the Hees et al. observations within a few tens of au to a = 1000 au. We also estimate the pericenter shift with a power-law potential V(r) ∼ 1/r 2 arising in five-dimensional gravity and obtain allowed ranges of the five-dimensional Planck mass through existing bounds on the parameterized post-Newtonian parameters coming from the orbits of S-2, S-38, and S-55. The breaking point for GR arises for a five-dimensional Planck mass of about 104 GeV. Constraint on this parameter, expected from the astrometric capabilities of existing and upcoming large telescopes, is also presented.

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Yekta, Davood Mahdavian, Seyed Aliasghar Alavi, and Majid Karimabadi. "Gravitational Measurements in Higher Dimensions." Galaxies 9, no. 1 (January 11, 2021): 4. http://dx.doi.org/10.3390/galaxies9010004.

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We attempt to study three significant tests of general relativity in higher dimensions, both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of Einstein’s equation in higher dimensions, with a source given by a static, spherically symmetric Gaussian distribution of mass. The resulting metric would describe a regular or curvature singularity free black hole in higher dimensions. The metric should smoothly interpolate between Schwarzschild geometry at large distance, and de-Sitter spacetime at short distance. We will consider gravitational redshift, lensing, and time delay in each sector. It will be shown that, compared to the four-dimensional spacetime, there can be significant modifications due to the presence of extra dimensions and the non-commutative corrected black holes. Finally, we shall attempt to obtain a lower bound on the size of the extra dimensions and on the mass needed to form a black hole in different dimensions.

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BENGTSSON, INGEMAR. "SOME REMARKS ON SPACE-TIME DECOMPOSITIONS, AND DEGENERATE METRICS, IN GENERAL RELATIVITY." International Journal of Modern Physics A 04, no. 20 (December 1989): 5527–38. http://dx.doi.org/10.1142/s0217751x89002363.

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Space-time decomposition of the Hilbert-Palatini action, written in a form which admits degenerate metrics, is considered. Simple numerology shows why D = 3 and 4 are singled out as admitting a simple phase space. The canonical structure of the degenerate sector turns out to be awkward. However, the real degenerate metrics obtained as solutions are the same as those that occur in Ashtekar's formulation of complex general relativity. An exact solution of Ashtekar's equations, with degenerate metric, shows that the manifestly four-dimensional form of the action, and its 3 + 1 form, are not quite equivalent.

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Kiy, Güliz, and Sezgin Aygün. "Higher-dimensional energy–momentum problem for Bianchi types V and I universes in gravitation theories." International Journal of Geometric Methods in Modern Physics 12, no. 04 (April 2015): 1550045. http://dx.doi.org/10.1142/s0219887815500450.

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Using the Einstein, Bergmann–Thomson, Landau–Lifshitz, Møller, Papapetrou and Tolman energy–momentum complexes in general relativity (GR) and teleparallel gravity (TG), we calculate the total energy–momentum distributions associated with N-dimensional Bianchi type V universe. While the solutions of Einstein, Bergmann–Thomson and Tolman energy and momentum densities are the same as each other, the solutions of Landau–Lifshitz, Møller and Papapetrou energy–momentum densities are different for N-dimensional Bianchi type V space-time in GR and TG. Obtained results for Einstein, Bergmann–Thomson and Landau–Lifshitz definitions we could say that GR and TG are in the same class. Because different energy–momentum distributions provide same results. However we have discussed N-dimensional Bianchi type I solutions and then we obtained all energy–momentum solutions are vanish in GR and TG theories. These results agree with Banerjee–Sen, Xulu, Aydoḡdu–Saltı and Radinschi in four dimensions.

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ALIEV, A. N. "A SLOWLY ROTATING CHARGED BLACK HOLE IN FIVE DIMENSIONS." Modern Physics Letters A 21, no. 09 (March 21, 2006): 751–57. http://dx.doi.org/10.1142/s0217732306019281.

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Black hole solutions in higher dimensional Einstein and Einstein–Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild, Reissner–Nordström and Kerr solutions of four-dimensional general relativity. However, higher dimensional generalization of the Kerr–Newman solution in four dimensions has not been found yet. As a first step in this direction we shall report on a new solution of the Einstein–Maxwell system of equations that describes an electrically charged and slowly rotating black hole in five dimensions.

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