Abstract
Strong cosmic censorship conjecture has been one of the most important leap of faith in the context of general relativity, providing assurance in the deterministic nature of the associated field equations. Though it holds well for asymptotically flat spacetimes, a potential failure of the strong cosmic censorship conjecture might arise for spacetimes inheriting Cauchy horizon along with a positive cosmological constant. We have explicitly demonstrated that violation of the censorship conjecture holds true in the presence of a Maxwell field even when higher spacetime dimensions are invoked. In particular, for a higher dimensional Reissner-Nordström-de Sitter black hole the violation of cosmic censorship conjecture is at a larger scale compared to the four dimensional one, for certain choices of the cosmological constant. On the other hand, for a brane world black hole, the effect of extra dimension is to make the violation of cosmic censorship conjecture weaker. For rotating black holes, intriguingly, the cosmic censorship conjecture is always respected even in presence of higher dimensions. A similar scenario is also observed for a rotating black hole on the brane.
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References
R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965) 57 [INSPIRE].
R.M. Wald, General relativity, Chicago Univ. Press, Chicago, IL, U.S.A. (1984) [INSPIRE].
P.T. Chrusciel ed., On uniqueness in the large of solutions of Einstein’s equations: “strong cosmic censorship”, Centre for Mathematics and its Applications, ANU, Canberra, ACT, Australia (1991).
J.L. Costa, P.M. Girão, J. Natário and J.D. Silva, On the occurrence of mass inflation for the Einstein-Maxwell-scalar field system with a cosmological constant and an exponential price law, Commun. Math. Phys. 361 (2018) 289 [arXiv:1707.08975] [INSPIRE].
J.L. Costa, P.M. Girão, J. Natário and J.D. Silva, On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion, Class. Quant. Grav. 32 (2015) 015017 [arXiv:1406.7245] [INSPIRE].
S. Chandrasekhar, The mathematical theory of black holes, Oxford classic texts in the physical sciences, Oxford Univ. Press, Oxford, U.K. (2002).
E. Poisson, A relativist’s toolkit: the mathematics of black-hole mechanics, Cambridge University Press, Cambridge, U.K. (2004) [INSPIRE].
M. Simpson and R. Penrose, Internal instability in a Reissner-Nordström black hole, Int. J. Theor. Phys. 7 (1973) 183 [INSPIRE].
E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev. D 41 (1990) 1796 [INSPIRE].
M. Dafermos, The interior of charged black holes and the problem of uniqueness in general relativity, Commun. Pure Appl. Math. 58 (2005) 0445 [gr-qc/0307013] [INSPIRE].
M. Dafermos, Black holes without spacelike singularities, Commun. Math. Phys. 332 (2014) 729 [arXiv:1201.1797] [INSPIRE].
A. Ori, Inner structure of a charged black hole: an exact mass-inflation solution, Phys. Rev. Lett. 67 (1991) 789 [INSPIRE].
D. Christodoulou, On the global initial value problem and the issue of singularities, Class. Quant. Grav. 16 (1999) A23.
V. Cardoso, J.L. Costa, K. Destounis, P. Hintz and A. Jansen, Quasinormal modes and strong cosmic censorship, Phys. Rev. Lett. 120 (2018) 031103 [arXiv:1711.10502] [INSPIRE].
D. Christodoulou, The formation of black holes in general relativity, in On recent developments in theoretical and experimental general relativity, astrophysics and relativistic field theories. Proceedings, 12th Marcel Grossmann Meeting on General Relativity, Paris, France, 12–18 July 2009, volume 1–3, World Scientific, Singapore (2008), pg. 24 [arXiv:0805.3880] [INSPIRE].
C.M. Chambers, The Cauchy horizon in black hole de Sitter space-times, Annals Israel Phys. Soc. 13 (1997) 33 [gr-qc/9709025] [INSPIRE].
R.H. Price, Nonspherical perturbations of relativistic gravitational collapse. 1. Scalar and gravitational perturbations, Phys. Rev. D 5 (1972) 2419 [INSPIRE].
M. Dafermos, I. Rodnianski and Y. Shlapentokh-Rothman, Decay for solutions of the wave equation on Kerr exterior spacetimes III: the full subextremal case |a| < M, arXiv:1402.7034 [INSPIRE].
Y. Angelopoulos, S. Aretakis and D. Gajic, Late-time asymptotics for the wave equation on spherically symmetric, stationary spacetimes, Adv. Math. 323 (2018) 529 [arXiv:1612.01566] [INSPIRE].
R.A. Matzner, N. Zamorano and V.D. Sandberg, Instability of the Cauchy horizon of Reissner-Nordström black holes, Phys. Rev. D 19 (1979) 2821 [INSPIRE].
W.A. Hiscock, Evolution of the interior of a charged black hole, Phys. Lett. A 83 (1981) 110.
P.R. Brady, I.G. Moss and R.C. Myers, Cosmic censorship: as strong as ever, Phys. Rev. Lett. 80 (1998) 3432 [gr-qc/9801032] [INSPIRE].
P.R. Brady, C.M. Chambers, W. Krivan and P. Laguna, Telling tails in the presence of a cosmological constant, Phys. Rev. D 55 (1997) 7538 [gr-qc/9611056] [INSPIRE].
S. Dyatlov, Asymptotics of linear waves and resonances with applications to black holes, Commun. Math. Phys. 335 (2015) 1445 [arXiv:1305.1723] [INSPIRE].
J.-F. Bony and D. Häfner, Decay and non-decay of the local energy for the wave equation on the de Sitter-Schwarzschild metric, Commun. Math. Phys. 282 (2008) 697.
S. Dyatlov, Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes, Ann. H. Poincaré 13 (2012) 1101.
A. Ori, Strength of curvature singularities, Phys. Rev. D 61 (2000) 064016 [INSPIRE].
J.L. Costa, P.M. Girão, J. Natário and J.D. Silva, On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: mass inflation and extendibility of the solutions, arXiv:1406.7261 [INSPIRE].
P. Hintz and A. Vasy, Analysis of linear waves near the Cauchy horizon of cosmological black holes, J. Math. Phys. 58 (2017) 081509 [arXiv:1512.08004] [INSPIRE].
M. Dafermos and J. Luk, The interior of dynamical vacuum black holes I: the C 0 -stability of the Kerr Cauchy horizon, arXiv:1710.01722 [INSPIRE].
O.J.C. Dias, F.C. Eperon, H.S. Reall and J.E. Santos, Strong cosmic censorship in de Sitter space, Phys. Rev. D 97 (2018) 104060 [arXiv:1801.09694] [INSPIRE].
R. Emparan and H.S. Reall, Black holes in higher dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
H.S. Reall, Higher dimensional black holes, Int. J. Mod. Phys. D 21 (2012) 1230001 [arXiv:1210.1402] [INSPIRE].
R. Emparan and H.S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The phase structure of higher-dimensional black rings and black holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [INSPIRE].
G. Arcioni and E. Lozano-Tellechea, Stability and critical phenomena of black holes and black rings, Phys. Rev. D 72 (2005) 104021 [hep-th/0412118] [INSPIRE].
G.W. Gibbons, D. Ida and T. Shiromizu, Uniqueness and nonuniqueness of static black holes in higher dimensions, Phys. Rev. Lett. 89 (2002) 041101 [hep-th/0206049] [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
G.T. Horowitz ed., Black holes in higher dimensions, Cambridge Univ. Pr., Cambridge, U.K. (2012) [INSPIRE].
R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].
T. Shiromizu, K.-I. Maeda and M. Sasaki, The Einstein equation on the 3-brane world, Phys. Rev. D 62 (2000) 024012 [gr-qc/9910076] [INSPIRE].
R. Maartens, Geometry and dynamics of the brane world, in Spanish relativity meeting on reference frames and gravitomagnetism (EREs2000), Valladolid, Spain, 6-9 September 2000, World Scientific, Sigapore (2001) [gr-qc/0101059] [INSPIRE].
N. Dadhich, R. Maartens, P. Papadopoulos and V. Rezania, Black holes on the brane, Phys. Lett. B 487 (2000) 1 [hep-th/0003061] [INSPIRE].
C. Germani and R. Maartens, Stars in the brane world, Phys. Rev. D 64 (2001) 124010 [hep-th/0107011] [INSPIRE].
R. Casadio and J. Ovalle, Brane-world stars and (microscopic) black holes, Phys. Lett. B 715 (2012) 251 [arXiv:1201.6145] [INSPIRE].
T. Harko and M.K. Mak, Vacuum solutions of the gravitational field equations in the brane world model, Phys. Rev. D 69 (2004) 064020 [gr-qc/0401049] [INSPIRE].
S. Chakraborty and S. SenGupta, Spherically symmetric brane spacetime with bulk f(R) gravity, Eur. Phys. J. C 75 (2015) 11 [arXiv:1409.4115] [INSPIRE].
S. Chakraborty and S. SenGupta, Effective gravitational field equations on m-brane embedded in n-dimensional bulk of Einstein and f(R) gravity, Eur. Phys. J. C 75 (2015) 538 [arXiv:1504.07519] [INSPIRE].
S. Chakraborty and S. SenGupta, Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet gravity, Class. Quant. Grav. 33 (2016) 225001 [arXiv:1510.01953] [INSPIRE].
S. Chakraborty, K. Chakravarti, S. Bose and S. SenGupta, Signatures of extra dimensions in gravitational waves from black hole quasinormal modes, Phys. Rev. D 97 (2018) 104053 [arXiv:1710.05188] [INSPIRE].
S. Mukherjee and S. Chakraborty, Horndeski theories confront the gravity probe B experiment, Phys. Rev. D 97 (2018) 124007 [arXiv:1712.00562] [INSPIRE].
I. Banerjee, S. Chakraborty and S. SenGupta, Excavating black hole continuum spectrum: possible signatures of scalar hairs and of higher dimensions, Phys. Rev. D 96 (2017) 084035 [arXiv:1707.04494] [INSPIRE].
S. Chakraborty and S. SenGupta, Strong gravitational lensing — a probe for extra dimensions and Kalb-Ramond field, JCAP 07 (2017) 045 [arXiv:1611.06936] [INSPIRE].
B. Mashhoon, Stability of charged rotating black holes in the eikonal approximation, Phys. Rev. D 31 (1985) 290 [INSPIRE].
N.J. Cornish and J.J. Levin, Lyapunov timescales and black hole binaries, Class. Quant. Grav. 20 (2003) 1649 [gr-qc/0304056] [INSPIRE].
V. Cardoso, A.S. Miranda, E. Berti, H. Witek and V.T. Zanchin, Geodesic stability, Lyapunov exponents and quasinormal modes, Phys. Rev. D 79 (2009) 064016 [arXiv:0812.1806] [INSPIRE].
L. Bombelli and E. Calzetta, Chaos around a black hole, Class. Quant. Grav. 9 (1992) 2573 [INSPIRE].
V. Ferrari and B. Mashhoon, Oscillations of a black hole, Phys. Rev. Lett. 52 (1984) 1361 [INSPIRE].
R.A. Konoplya and Z. Stuchlík, Are eikonal quasinormal modes linked to the unstable circular null geodesics?, Phys. Lett. B 771 (2017) 597 [arXiv:1705.05928] [INSPIRE].
S. Hod, Black-hole quasinormal resonances: wave analysis versus a geometric-optics approximation, Phys. Rev. D 80 (2009) 064004 [arXiv:0909.0314] [INSPIRE].
S. Hod, Strong cosmic censorship in charged black-hole spacetimes: as strong as ever, Nucl. Phys. B 941 (2019) 636 [arXiv:1801.07261] [INSPIRE].
V. Cardoso, J.L. Costa, K. Destounis, P. Hintz and A. Jansen, Strong cosmic censorship in charged black-hole spacetimes: still subtle, Phys. Rev. D 98 (2018) 104007 [arXiv:1808.03631] [INSPIRE].
B. Ge, J. Jiang, B. Wang, H. Zhang and Z. Zhong, Strong cosmic censorship for the massless Dirac field in the Reissner-Nordström-de Sitter spacetime, JHEP 01 (2019) 123 [arXiv:1810.12128] [INSPIRE].
Y. Mo, Y. Tian, B. Wang, H. Zhang and Z. Zhong, Strong cosmic censorship for the massless charged scalar field in the Reissner-Nordström-de Sitter spacetime, Phys. Rev. D 98 (2018) 124025 [arXiv:1808.03635] [INSPIRE].
D.-P. Du, B. Wang and R.-K. Su, Quasinormal modes in pure de Sitter space-times, Phys. Rev. D 70 (2004) 064024 [hep-th/0404047] [INSPIRE].
E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].
V. Cardoso, G. Siopsis and S. Yoshida, Scalar perturbations of higher dimensional rotating and ultra-spinning black holes, Phys. Rev. D 71 (2005) 024019 [hep-th/0412138] [INSPIRE].
D. Ida, Y. Uchida and Y. Morisawa, The scalar perturbation of the higher dimensional rotating black holes, Phys. Rev. D 67 (2003) 084019 [gr-qc/0212035] [INSPIRE].
A. Lopez-Ortega, On the quasinormal modes of the de Sitter spacetime, Gen. Rel. Grav. 44 (2012) 2387 [arXiv:1207.6791] [INSPIRE].
E. Abdalla, K.H.C. Castello-Branco and A. Lima-Santos, Support of dS/CFT correspondence from space-time perturbations, Phys. Rev. D 66 (2002) 104018 [hep-th/0208065] [INSPIRE].
Y.-W. Kim, Y.S. Myung and Y.-J. Park, Quasinormal modes and hidden conformal symmetry in the Reissner-Nordström black hole, Eur. Phys. J. C 73 (2013) 2440 [arXiv:1205.3701] [INSPIRE].
C.-M. Chen, S.P. Kim, I.-C. Lin, J.-R. Sun and M.-F. Wu, Spontaneous pair production in Reissner-Nordström black holes, Phys. Rev. D 85 (2012) 124041 [arXiv:1202.3224] [INSPIRE].
A. Chamblin, H.S. Reall, H.-A. Shinkai and T. Shiromizu, Charged brane world black holes, Phys. Rev. D 63 (2001) 064015 [hep-th/0008177] [INSPIRE].
R.-G. Cai, Cardy-Verlinde formula and thermodynamics of black holes in de Sitter spaces, Nucl. Phys. B 628 (2002) 375 [hep-th/0112253] [INSPIRE].
L.-C. Zhang, M.-S. Ma, H.-H. Zhao and R. Zhao, Thermodynamics of phase transition in higher-dimensional Reissner-Nordström-de Sitter black hole, Eur. Phys. J. C 74 (2014) 3052 [arXiv:1403.2151] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Instability of higher dimensional charged black holes in the de-Sitter world, Phys. Rev. Lett. 103 (2009) 161101 [arXiv:0809.2822] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Instability of D-dimensional extremally charged Reissner-Nordström(-de Sitter) black holes: extrapolation to arbitrary D, Phys. Rev. D 89 (2014) 024011 [arXiv:1309.7667] [INSPIRE].
G.N. Gyulchev and S.S. Yazadjiev, Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit, Phys. Rev. D 75 (2007) 023006 [gr-qc/0611110] [INSPIRE].
M. Rahman and A.A. Sen, Astrophysical signatures of black holes in generalized Proca theories, Phys. Rev. D 99 (2019) 024052 [arXiv:1810.09200] [INSPIRE].
G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The general Kerr-de Sitter metrics in all dimensions, J. Geom. Phys. 53 (2005) 49 [hep-th/0404008] [INSPIRE].
G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, Rotating black holes in higher dimensions with a cosmological constant, Phys. Rev. Lett. 93 (2004) 171102 [hep-th/0409155] [INSPIRE].
M.S. Modgil, S. Panda and G. Sengupta, Rotating brane world black holes, Mod. Phys. Lett. A 17 (2002) 1479 [hep-th/0104122] [INSPIRE].
V.P. Frolov, D.V. Fursaev and D. Stojkovic, Rotating black holes in brane worlds, JHEP 06 (2004) 057 [gr-qc/0403002] [INSPIRE].
A. Larrañaga, C. Grisales and M. Londoño, A topologically charged rotating black hole in the brane, Adv. High Energy Phys. 2013 (2013) 727294 [INSPIRE].
M. Dafermos and Y. Shlapentokh-Rothman, Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ > 0, Class. Quant. Grav. 35 (2018) 195010 [arXiv:1805.08764] [INSPIRE].
O.J.C. Dias, H.S. Reall and J.E. Santos, Strong cosmic censorship: taking the rough with the smooth, JHEP 10 (2018) 001 [arXiv:1808.02895] [INSPIRE].
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Rahman, M., Chakraborty, S., SenGupta, S. et al. Fate of strong cosmic censorship conjecture in presence of higher spacetime dimensions. J. High Energ. Phys. 2019, 178 (2019). https://doi.org/10.1007/JHEP03(2019)178
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DOI: https://doi.org/10.1007/JHEP03(2019)178