Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes. (English) Zbl 1485.83105
Summary: We study past-directed extendibility of Friedmann-Lemaître-Robertson-Walker (FLRW) and Bianchi type I spacetimes with a scale factor vanishing in the past. We give criteria for determining whether a boundary for past-directed incomplete geodesics is a parallelly propagated curvature singularity, which cannot necessarily be read off from scalar curvature invariants. It is clarified that, for incomplete FLRW spacetime to avoid the singularity, the spacetime necessarily reduces to the Milne universe or flat de Sitter universe toward the boundary. For incomplete Bianchi type I spacetime to be free of singularity, it is necessary that the spacetime asymptotically fits into the product of the extendible isotropic geometry (Milne or flat de Sitter) and flat space, or, anisotropic spacetime with specific power law scale factors. Furthermore, we investigate in detail the time-dependence of the scale factor compatible with the extendibility in both spacetimes beyond the leading order.
MSC:
| 83E05 | Geometrodynamics and the holographic principle |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 83F05 | Relativistic cosmology |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
| 58J32 | Boundary value problems on manifolds |
References:
| [1] | LIGO Scientific, Virgo Collaboration; Abbott, B. P., Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett., 116 (2016) · doi:10.1103/PhysRevLett.116.061102 |
| [2] | Event Horizon Telescope Collaboration; Akiyama, Kazunori, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. Lett., 875, L1 (2019) · doi:10.3847/2041-8213/ab0ec7 |
| [3] | Penrose, Roger, Gravitational collapse and space-time singularities, Phys. Rev. Lett., 14, 57-59 (1965) · Zbl 0125.21206 · doi:10.1103/PhysRevLett.14.57 |
| [4] | Hawking, S. W.; Penrose, R., The Singularities of gravitational collapse and cosmology, Proc. Roy. Soc. Lond. A, 314, 529-548 (1970) · Zbl 0954.83012 · doi:10.1098/rspa.1970.0021 |
| [5] | Hawking, Stephen, The occurrence of singularities in cosmology. III. Causality and singularities, Proc. Roy. Soc. Lond. A, 300, 187-201 (1967) · Zbl 0163.23903 · doi:10.1098/rspa.1967.0164 |
| [6] | Mukhanov, Viatcheslav F.; Brandenberger, Robert H., A Nonsingular universe, Phys. Rev. Lett., 68, 1969-1972 (1992) · Zbl 0969.83520 · doi:10.1103/PhysRevLett.68.1969 |
| [7] | Brandenberger, Robert H.; Mukhanov, Viatcheslav F.; Sornborger, A., A Cosmological theory without singularities, Phys. Rev. D, 48, 1629-1642 (1993) · doi:10.1103/PhysRevD.48.1629 |
| [8] | Moessner, R.; Trodden, M., Singularity - free two-dimensional cosmologies, Phys. Rev. D, 51, 2801-2807 (1995) · doi:10.1103/PhysRevD.51.2801 |
| [9] | Easson, Damien A., The Accelerating Universe and a Limiting Curvature Proposal, JCAP, 02 (2007) · Zbl 1181.83222 · doi:10.1088/1475-7516/2007/02/004 |
| [10] | Yoshida, Daisuke; Quintin, Jerome; Yamaguchi, Masahide; Brandenberger, Robert H., Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature, Phys. Rev. D, 96 (2017) · doi:10.1103/PhysRevD.96.043502 |
| [11] | Quintin, Jerome; Yoshida, Daisuke, Cuscuton gravity as a classically stable limiting curvature theory, JCAP, 02 (2020) · Zbl 1489.83070 · doi:10.1088/1475-7516/2020/02/016 |
| [12] | Sakakihara, Yuki; Yoshida, Daisuke; Takahashi, Kazufumi; Quintin, Jerome, Theories with limited extrinsic curvature and a nonsingular anisotropic universe, Phys. Rev. D, 102 (2020) · doi:10.1103/PhysRevD.102.084004 |
| [13] | Trodden, M.; Mukhanov, Viatcheslav F.; Brandenberger, Robert H., A Nonsingular two-dimensional black hole, Phys. Lett. B, 316, 483-487 (1993) · doi:10.1016/0370-2693(93)91032-I |
| [14] | Easson, Damien A., Hawking radiation of nonsingular black holes in two-dimensions, JHEP, 02, 037 (2003) · doi:10.1088/1126-6708/2003/02/037 |
| [15] | Yoshida, Daisuke; Brandenberger, Robert H., Singularities in Spherically Symmetric Solutions with Limited Curvature Invariants, JCAP, 07 (2018) · Zbl 1527.83069 · doi:10.1088/1475-7516/2018/07/022 |
| [16] | Jonas, Caroline; Lehners, Jean-Luc; Quintin, Jerome, Cosmological consequences of a principle of finite amplitudes, Phys. Rev. D, 103 (2021) · doi:10.1103/PhysRevD.103.103525 |
| [17] | J. Bardeen, Non-singular general-relativistic gravitational collapse, in proceedings of the International Conference GR5, Tbilisi, USSR, 9-13 September 1968. |
| [18] | Borde, Arvind, Regular black holes and topology change, Phys. Rev. D, 55, 7615-7617 (1997) · doi:10.1103/PhysRevD.55.7615 |
| [19] | Hayward, Sean A., Formation and evaporation of regular black holes, Phys. Rev. Lett., 96 (2006) · Zbl 1087.83022 · doi:10.1103/PhysRevLett.96.031103 |
| [20] | Bronnikov, K. A.; Fabris, J. C., Regular phantom black holes, Phys. Rev. Lett., 96 (2006) · Zbl 1228.83063 · doi:10.1103/PhysRevLett.96.251101 |
| [21] | Bronnikov, K. A.; Melnikov, V. N.; Dehnen, Heinz, Regular black holes and black universes, Gen. Rel. Grav., 39, 973-987 (2007) · Zbl 1157.83328 · doi:10.1007/s10714-007-0430-6 |
| [22] | Ansoldi, Stefano, Spherical black holes with regular center: A Review of existing models including a recent realization with Gaussian sources (2008) |
| [23] | Bambi, Cosimo; Modesto, Leonardo, Rotating regular black holes, Phys. Lett. B, 721, 329-334 (2013) · Zbl 1309.83058 · doi:10.1016/j.physletb.2013.03.025 |
| [24] | Ayon-Beato, Eloy; Garcia, Alberto, The Bardeen model as a nonlinear magnetic monopole, Phys. Lett. B, 493, 149-152 (2000) · Zbl 0976.81127 · doi:10.1016/S0370-2693(00)01125-4 |
| [25] | Bronnikov, Kirill A., Regular magnetic black holes and monopoles from nonlinear electrodynamics, Phys. Rev. D, 63 (2001) · doi:10.1103/PhysRevD.63.044005 |
| [26] | Moreno, Claudia; Sarbach, Olivier, Stability properties of black holes in selfgravitating nonlinear electrodynamics, Phys. Rev. D, 67 (2003) · doi:10.1103/PhysRevD.67.024028 |
| [27] | Fan, Zhong-Ying; Wang, Xiaobao, Construction of Regular Black Holes in General Relativity, Phys. Rev. D, 94 (2016) · doi:10.1103/PhysRevD.94.124027 |
| [28] | Nomura, Kimihiro; Yoshida, Daisuke; Soda, Jiro, Stability of magnetic black holes in general nonlinear electrodynamics, Phys. Rev. D, 101 (2020) · doi:10.1103/PhysRevD.101.124026 |
| [29] | Ellis, G. F. R.; Schmidt, B. G., Singular space-times, Gen. Rel. Grav., 8, 915-953 (1977) · Zbl 0434.53048 · doi:10.1007/BF00759240 |
| [30] | S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time. Volume 1, Cambridge University Press, Cambridge U.K. (1973). · Zbl 0265.53054 |
| [31] | C.J.S. Clarke, Local extensions in singular space-times, Commun. Math. Phys.32 (1973) 205. · Zbl 0259.53047 · doi:10.1007/BF01645592 |
| [32] | Ellis, G. F. R.; King, A. R., Was the big bang a whimper?, Commun. Math. Phys., 38, 119-156 (1974) · doi:10.1007/BF01651508 |
| [33] | Clarke, C. J. S., Singularities in globally hyperbolic space-time, Commun. Math. Phys., 41, 65-78 (1975) · Zbl 0306.53060 · doi:10.1007/BF01608548 |
| [34] | C.J.S. Clarke, Local extensions in singular space-times II, Commun. Math. Phys.84 (1982) 329. · Zbl 0495.53015 · doi:10.1007/BF01208481 |
| [35] | Borde, Arvind; Guth, Alan H.; Vilenkin, Alexander, Inflationary space-times are incompletein past directions, Phys. Rev. Lett., 90 (2003) · doi:10.1103/PhysRevLett.90.151301 |
| [36] | Yoshida, Daisuke; Quintin, Jerome, Maximal extensions and singularities in inflationary spacetimes, Class. Quant. Grav., 35 (2018) · Zbl 1409.83241 · doi:10.1088/1361-6382/aacf4b |
| [37] | Fernández-Jambrina, L., Hidden past of dark energy cosmological models, Phys. Lett. B, 656, 9-14 (2007) · Zbl 1246.83255 · doi:10.1016/j.physletb.2007.08.091 |
| [38] | Fernández-Jambrina, L., Initial directional singularity in inflationary models, Phys. Rev. D, 94 (2016) · doi:10.1103/PhysRevD.94.024049 |
| [39] | Belinsky, V. A.; Khalatnikov, I. M.; Lifshitz, E. M., Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys., 19, 525-573 (1970) · doi:10.1080/00018737000101171 |
| [40] | L.D. Landau, The classical theory of fields. Volume 2, Elsevier (2013). |
| [41] | Ashtekar, Abhay; Henderson, Adam; Sloan, David, A Hamiltonian Formulation of the BKL Conjecture, Phys. Rev. D, 83 (2011) · doi:10.1103/PhysRevD.83.084024 |
| [42] | Fernández-Jambrina, L.; Lazkoz, R., Classification of cosmological milestones, Phys. Rev. D, 74 (2006) · doi:10.1103/PhysRevD.74.064030 |
| [43] | Cataldo, Mauricio; Cid, Antonella; Labraña, Pedro; Mella, Patricio, Cosmic anisotropic doomsday in Bianchi type I universes, J. Math. Phys., 57 (2016) · Zbl 1354.83018 · doi:10.1063/1.4967954 |
| [44] | Numasawa, Tokiro; Yoshida, Daisuke, Global Spacetime Structure of Compactified Inflationary Universe, Class. Quant. Grav., 36 (2019) · Zbl 1478.83261 · doi:10.1088/1361-6382/ab38ed |
| [45] | Harada, Tomohiro; Carr, B. J.; Igata, Takahisa, Complete conformal classification of the Friedmann-Lemaître-Robertson-Walker solutions with a linear equation of state, Class. Quant. Grav., 35 (2018) · Zbl 1391.83024 · doi:10.1088/1361-6382/aab99f |
| [46] | Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet, Quantum nature of the big bang, Phys. Rev. Lett., 96 (2006) · Zbl 1153.83417 · doi:10.1103/PhysRevLett.96.141301 |
| [47] | Bojowald, Martin, Loop quantum cosmology, Living Rev. Rel., 8, 11 (2005) · Zbl 1255.83133 · doi:10.12942/lrr-2005-11 |
| [48] | Ashtekar, Abhay; Wilson-Ewing, Edward, Loop quantum cosmology of Bianchi I models, Phys. Rev. D, 79 (2009) · doi:10.1103/PhysRevD.79.083535 |
| [49] | Singh, Parampreet, Curvature invariants, geodesics and the strength of singularities in Bianchi-I loop quantum cosmology, Phys. Rev. D, 85 (2012) · Zbl 1260.83003 · doi:10.1103/PhysRevD.85.104011 |
| [50] | Blau, Matthias; Figueroa-O’Farrill, Jose M.; Papadopoulos, George, Penrose limits, supergravity and brane dynamics, Class. Quant. Grav., 19, 4753 (2002) · Zbl 1026.83057 · doi:10.1088/0264-9381/19/18/310 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
