×

Gravitational collapse and singularity removal in Rastall theory. (English) Zbl 1457.83047

Summary: In the present work, we study spherically symmetric gravitational collapse of a homogeneous fluid in the framework of Rastall gravity. Considering a nonlinear equation of state (EoS) for the fluid profiles, we search for a class of nonsingular collapse solutions and the possibility of singularity removal. We find that depending on the model parameters, the collapse scenario halts at a minimum value of the scale factor at which a bounce occurs. The collapse process then enters an expanding phase in the postbounce regime, and consequently the formation of a spacetime singularity is prevented. We also find that, in comparison to the singular case where the apparent horizon forms to cover the singularity, the formation of apparent horizon can be delayed allowing thus the bounce to be causally connected to the external universe. The nonsingular solutions we obtain satisfy the weak energy condition (WEC) which is crucial for physical validity of the model.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C75 Space-time singularities, cosmic censorship, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hawking, S. W.; Ellis, G. F. R., The Large Scale Structure of Space-Time (1973), Cambridge University Press · Zbl 0265.53054
[2] Joshi, P. S.; Malafarina, D., Recent developments in gravitational collapse and spacetime singularities, International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 20, 14, 2641-2729 (2011) · Zbl 1263.83011 · doi:10.1142/S0218271811020792
[3] Penrose, R., Gravitational collapse: the role of general relativity, Nuovo Cimento Rivista Serie, 1, 252 (1969)
[4] Penrose, R., “Golden Oldie”: gravitational collapse: the role of general relativity, General Relativity and Gravitation, 34, 7, 1141-1165 (2002) · Zbl 1001.83040
[5] Wald, R. M., Black holes and relativistic stars (1998), University of Chicago Press
[6] Joshi, P. S., Spacetime singularities, Springer Handbook of Spacetime, 409 (2014), Germany: Springer Berlin Heidelberg, Germany · doi:10.1007/978-3-642-41992-8_20
[7] Ong, Y. C., Space-time singularities and cosmic censorship conjecture: a review with some thoughts, International Journal of Modern Physics A: Particles and Fields; Gravitation; Cosmology; Nuclear Physics, 35, 14, article 2030007 (2020) · doi:10.1142/S0217751X20300070
[8] Joshi, P. S., Global Aspects in Gravitation and Cosmology (1993), Oxford: Oxford University Press, Oxford · Zbl 0853.53055
[9] Joshi, P. S., Gravitational Collapse and Space-Time Singularities (2007), Cambridge: Cambridge University Press, Cambridge · Zbl 1135.83002 · doi:10.1017/CBO9780511536274
[10] Deshingkar, S. S.; Jhingan, S.; Chamorro, A.; Joshi, P. S., Gravitational collapse and the cosmological constant, Physical Review D, 63, 12, article 124005 (2001) · doi:10.1103/PhysRevD.63.124005
[11] Miyamoto, U.; Nemoto, H.; Shimano, M., Naked singularity explosion in higher dimensions, Physical Review D, 84, 6, article 064045 (2011) · doi:10.1103/PhysRevD.84.064045
[12] Dadhich, N.; Ghosh, S. G.; Jhingan, S., Gravitational collapse in pure Lovelock gravity in higher dimensions, Physical Review D, 88, 8, article 084024 (2013) · doi:10.1103/PhysRevD.88.084024
[13] Shimano, M.; Miyamoto, U., Naked singularity explosion in higher-dimensional dust collapse, Classical and Quantum Gravity, 31, 4, article 045002 (2014) · Zbl 1286.83072 · doi:10.1088/0264-9381/31/4/045002
[14] Ghosh, S. G.; Beesham, A., Naked singularities in higher dimensional inhomogeneous dust collapse, Classical and Quantum Gravity, 17, 24, 4959-4965 (2000) · Zbl 0972.83066 · doi:10.1088/0264-9381/17/24/301
[15] Giambo, R., Gravitational collapse of homogeneous perfect fluids in higher order gravity theories, Journal of Mathematical Physics, 50, 1, article 012501 (2009) · Zbl 1189.83047 · doi:10.1063/1.3032755
[16] Roberts, M. D., Scalar field counterexamples to the cosmic censorship hypothesis, General relativity and gravitation, 21, 9, 907-939 (1989) · Zbl 0676.53093 · doi:10.1007/BF00769864
[17] Brady, P. R., Self-similar scalar field collapse: naked singularities and critical behavior, Physical Review D, 51, 8, 4168-4176 (1995) · doi:10.1103/PhysRevD.51.4168
[18] Choptuik, M. W., Universality and scaling in gravitational collapse of a massless scalar field, Physical Review Letters, 70, 1, 9-12 (1993) · doi:10.1103/PhysRevLett.70.9
[19] Husain, V.; Martinez, E. A.; Nunez, D., Exact solution for scalar field collapse, Physical Review D, 50, 6, 3783-3786 (1994) · doi:10.1103/PhysRevD.50.3783
[20] Ganguly, K.; Banerjee, N., Pramana, Journal de Physique, 80, 3, 439-448 (2013)
[21] Joshi, P. S.; Dwivedi, I. H., The structure of naked singularity in self-similar gravitational collapse, Communications in Mathematical Physics, 146, 2, 333-342 (1992) · Zbl 0764.53053 · doi:10.1007/BF02102631
[22] Brandt, C. F. C.; Chan, R.; Da Silva, M. F. A.; Villas da Rocha, J. F., Gravitational collapse of an anisotropic fluid with self-similarity of the second kind, International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 15, 9, 1407-1417 (2006) · Zbl 1152.83373
[23] Brandt, C. F. C.; Lin, L.-M.; Villas da Rocha, J. F.; Wang, A. Z., Gravitational collapse of spherically symmetric perfect fluid with kinematic self-similarity, International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 11, 2, 155-186 (2002) · Zbl 1070.83520 · doi:10.1142/S0218271802001500
[24] Garattini, R., Naked singularity in modified gravity theory, Journal of Physics Conference Series, 174, article 012066 (2009) · doi:10.1088/1742-6596/174/1/012066
[25] Ziaie, A. H.; Atazadeh, K.; Tavakoli, Y., Naked singularity formation in Brans-Dicke theory, Classical and quantum gravity, 27, 7, article 075016 (2010) · Zbl 1187.83067 · doi:10.1088/0264-9381/27/7/075016
[26] Ziaie, A. H.; Atazadeh, K.; Rasouli, S. M. M., Naked singularity formation in \(f\left( \mathcal{R}\right)\) gravity, General Relativity and Gravitation, 43, 11, 2943-2963 (2011) · Zbl 1228.83087 · doi:10.1007/s10714-011-1216-4
[27] Ghosh, S. G.; Maharaj, S. D., Gravitational collapse of null dust inf(R)gravity, Physical Review D, 85, 12, 124064 (2012) · doi:10.1103/PhysRevD.85.124064
[28] Ziaie, A. H.; Ranjbar, A.; Sepangi, H. R., Trapped surfaces and the nature of singularity in Lyra’s geometry, Classical and Quantum Gravity, 32, 2, article 025010 (2015) · Zbl 1307.83041 · doi:10.1088/0264-9381/32/2/025010
[29] Abbas, G.; Tahir, M., Gravitational perfect fluid collapse in Gauss-Bonnet gravity, European Physical Journal C: Particles and Fields, 77, 8, 537 (2017) · doi:10.1140/epjc/s10052-017-5114-0
[30] Shaikh, R.; Joshi, P. S., Gravitational collapse in (2+1)-dimensional Eddington-inspired Born-Infeld gravity, Physical Review D, 98, 2, article 024033 (2018) · doi:10.1103/PhysRevD.98.024033
[31] Bambi, C.; Malafarina, D.; Modesto, L., Non-singular quantum-inspired gravitational collapse, Physical Review D, 88, 4, article 044009 (2013) · doi:10.1103/PhysRevD.88.044009
[32] Bojowald, M.; Goswami, R.; Maartens, R.; Singh, P., Black hole mass threshold from nonsingular quantum gravitational collapse, Physical Review Letters, 95, 9, article 091302 (2005) · doi:10.1103/PhysRevLett.95.091302
[33] Goswami, R.; Joshi, P. S.; Singh, P., Quantum evaporation of a naked singularity, Physical Review Letters, 96, 3, article 031302 (2006) · doi:10.1103/PhysRevLett.96.031302
[34] Tavakoli, Y.; Marto, J.; Dapor, A., Semiclassical dynamics of horizons in spherically symmetric collapse, International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 23, 7, article 1450061 (2014) · doi:10.1142/S0218271814500618
[35] Bambi, C.; Malafarina, D.; Modesto, L., Terminating black holes in asymptotically free quantum gravity, European Physical Journal C: Particles and Fields, 74, 2, 2767 (2014) · doi:10.1140/epjc/s10052-014-2767-9
[36] Barcelo, C.; Liberati, S.; Sonego, S.; Visser, M., Fate of gravitational collapse in semiclassical gravity, Physical Review D, 77, 4, article 044032 (2008) · doi:10.1103/PhysRevD.77.044032
[37] Tavakoli, Y.; Escamilla-Rivera, C.; Fabris, J. C., The final state of gravitational collapse in Eddington-inspired Born-Infeld theory, Annalen der Physik, 529, 5, article 1600415 (2017) · Zbl 1365.83027 · doi:10.1002/andp.201600415
[38] Bamba, K.; Odintsov, S. D.; Sebastiani, L.; Zerbini, S., Finite-time future singularities in modified Gauss-Bonnet and ℱ(R,G) gravity and singularity avoidance, European Physical Journal C: Particles and Fields, 67, 1-2, 295-310 (2010) · doi:10.1140/epjc/s10052-010-1292-8
[39] Gorbunova, O.; Sebastiani, L., Viscous fluids and Gauss-Bonnet modified gravity, General Relativity and Gravitation, 42, 12, 2873-2890 (2010) · Zbl 1204.83068 · doi:10.1007/s10714-010-1031-3
[40] Misonoh, Y.; Fukushima, M.; Miyashita, S., Stability of singularity-free cosmological solutions in Hořava-Lifshitz gravity, Physical Review D, 95, 4, article 044044 (2017) · doi:10.1103/PhysRevD.95.044044
[41] Bambi, C.; Malafarina, D.; Marciano, A.; Modesto, L., Singularity avoidance in classical gravity from four-fermion interaction, Physics Letters B, 734, 27-30 (2014) · Zbl 1380.83170 · doi:10.1016/j.physletb.2014.05.013
[42] Myrzakulov, R.; Sebastiani, L.; Zerbini, S., Some aspects of generalized modified gravity models, International Journal of Modern Physics D: Gravitation; Astrophysics and Cosmology, 22, 8, article 1330017 (2013) · Zbl 1277.85002 · doi:10.1142/S0218271813300176
[43] Lobo, F. S. N., Beyond Einstein’s general relativity, Journal of Physics Conference Series, 600, article 012006 (2015) · doi:10.1088/1742-6596/600/1/012006
[44] Faraoni, V.; Capozziello, S.; Capozziello, S.; Faraoni, V., The landscape beyond Einstein gravity, Beyond Einstein Gravity, 59-106 (2011), Dordrecht: Springer, Dordrecht · doi:10.1007/978-94-007-0165-6_3
[45] Birrell, N. D.; Davies, P. C. W., Quantum Fields in Curved Space (1982), Cambridge: Cambridge University Press, Cambridge · Zbl 0476.53017
[46] Gibbons, G. W.; Hawking, S. W., Cosmological event horizons, thermodynamics, and particle creation, Physical Review D, 15, 10, 2738-2751 (1977) · doi:10.1103/PhysRevD.15.2738
[47] Parker, L., Quantized fields and particle creation in expanding universes. II, Physical Review D, 3, 2, 346-356 (1971) · doi:10.1103/PhysRevD.3.346
[48] Ford, L. H., Gravitational particle creation and inflation, Physical Review D, 35, 10, 2955-2960 (1987) · doi:10.1103/PhysRevD.35.2955
[49] Nojiri, S.; Odintsov, S. D., Gravity assisted dark energy dominance and cosmic acceleration, Physics Letters B, 599, 3-4, 137-142 (2004) · doi:10.1016/j.physletb.2004.08.045
[50] Allemandi, G.; Borowiec, A.; Francaviglia, M.; Odintsov, S. D., Dark energy dominance and cosmic acceleration in first-order formalism, Physical Review D, 72, 6, article 063505 (2005) · doi:10.1103/PhysRevD.72.063505
[51] Koivisto, T., A note on covariant conservation of energy-momentum in modified gravities, Classical and Quantum Gravity, 23, 12, 4289-4296 (2006) · Zbl 1096.83056 · doi:10.1088/0264-9381/23/12/N01
[52] Bertolami, O.; Böhmer, C. G.; Harko, T.; Lobo, F. S. N., Extra force in f(R) modified theories of gravity, Physical Review D, 75, 10, article 104016 (2007) · doi:10.1103/PhysRevD.75.104016
[53] Harko, T.; Lobo, F. S. N., Generalized curvature-matter couplings in modified gravity, Galaxies, 2, 3, 410-465 (2014) · doi:10.3390/galaxies2030410
[54] Rastall, P., Generalization of the Einstein theory, Physical Review D, 6, 12, 3357-3359 (1972) · Zbl 0959.83525 · doi:10.1103/PhysRevD.6.3357
[55] Moradpour, H.; Heydarzade, Y.; Darabi, F.; Salako, I. G., A generalization to the Rastall theory and cosmic eras, European Physical Journal C: Particles and Fields, 77, 4, 259 (2017) · doi:10.1140/epjc/s10052-017-4811-z
[56] Darabi, F.; Moradpour, H.; Licata, I.; Heydarzade, Y.; Corda, C., Einstein and Rastall theories of gravitation in comparison, The European Physical Journal C, 78, 1 (2018) · doi:10.1140/epjc/s10052-017-5502-5
[57] Al-Rawaf, A. S.; Taha, M. O., A resolution of the cosmological age puzzle, Physics Letters B, 366, 1-4, 69-71 (1996) · doi:10.1016/0370-2693(95)01145-5
[58] Al-Rawaf, A. S.; Taha, M. O., Cosmology of general relativity without energy-momentum conservation, General Relativity and Gravitation, 28, 8, 935-952 (1996) · Zbl 0875.83034 · doi:10.1007/BF02113090
[59] Moradpour, H.; Sadeghnezhad, N.; Hendi, S. H., Traversable asymptotically flat wormholes in Rastall gravity, Canadian Journal of Physics, 95, 12, 1257-1266 (2017) · doi:10.1139/cjp-2017-0040
[60] Bronnikov, K. A.; Fabris, J. C.; Piattella, O. F.; Santos, E. C., Static, spherically symmetric solutions with a scalar field in Rastall gravity, General Relativity and Gravitation, 48, 12, 162 (2016) · Zbl 1370.83072 · doi:10.1007/s10714-016-2152-0
[61] Oppenheimer, J. R.; Snyder, H., On continued gravitational contraction, Physics Review, 56, 5, 455-459 (1939) · Zbl 0022.28104 · doi:10.1103/PhysRev.56.455
[62] Datt, S., Über eine klasse von Lösungen der gravitationsgleichungen der relativität, Zeitschrift für Physik, 108, 5-6, 314-321 (1938) · Zbl 0018.18606 · doi:10.1007/BF01374951
[63] Baumgarte, T. W.; Shapiro, S. L., Numerical relativity: solving Einstein’s equations on the computer (2010), Cambridge: Cambridge University Press, Cambridge · Zbl 1198.83001 · doi:10.1017/CBO9781139193344
[64] Ziaie, A. H.; Moradpour, H.; Ghaffari, S., Gravitational collapse in Rastall gravity, Physics Letters B, 793, 276-280 (2019) · Zbl 1421.83092 · doi:10.1016/j.physletb.2019.04.055
[65] Hashemi, M.; Jalalzadeh, S.; Ziaie, A. H., Collapse and dispersal of a homogeneous spin fluid in Einstein-Cartan theory, European Physical Journal C: Particles and Fields, 75, 2, 53 (2015) · doi:10.1140/epjc/s10052-015-3276-1
[66] Vaidya, P. C., The gravitational field of a radiating star, Proceedings of the Indian Academy of Sciences-Section A, 33, 5, 264 (1951) · Zbl 0044.42202 · doi:10.1007/BF03173260
[67] Santos, N. O., Non-adiabatic radiating collapse, Monthly Notices of the Royal Astronomical Society, 216, 2, 403-410 (1985) · doi:10.1093/mnras/216.2.403
[68] Bonnor, W. B.; de Oliveira, A. K. G.; Santos, N. O., Radiating spherical collapse, Physics Reports, 181, 5, 269-326 (1989) · doi:10.1016/0370-1573(89)90069-0
[69] Israel, W., Singular hypersurfaces and thin shells in general relativity, Il Nuovo Cimento B (1965-1970), 44, 1, 1-14 (1966) · doi:10.1007/BF02710419
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.