×

Numerical evolution of the interior geometry of charged black holes. (English) Zbl 1483.83038

Summary: Previously, we developed a late time approximation scheme to study the interior geometry of black holes. In the present paper we test this scheme with numerical relativity simulations. In particular, we present numerical relativity simulations of the interior geometry of charged spherically symmetric two-sided black holes with a spacelike singularity at \(r=0\). Our numerics are in excellent agreement with the late time approximatoin. We also demonstrate that the geometry near \(r=0\) is a scalarized Kasner geometry and compute the associated Kasner exponents.

MSC:

83C57 Black holes
83C75 Space-time singularities, cosmic censorship, etc.
83-10 Mathematical modeling or simulation for problems pertaining to relativity and gravitational theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Price, RH, Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations, Phys. Rev. D, 5, 2419-2438 (1972)
[2] Price, RH, Nonspherical perturbations of relativistic gravitational collapse. II. integer-spin, zero-rest-mass fields, Phys. Rev. D, 5, 2439-2454 (1972)
[3] R. Penrose, Structure of space-time. In: DeWitt, C.M., Wheeler, J.A. (eds.) Battelle Rencontres: 1967 Lectures in Mathematics and Physics, pp. 121-235. Benjamin, New York (1968) · Zbl 0174.55901
[4] Simpson, M.; Penrose, R., Internal instability in a Reissner-Nordstrom black hole, Int. J. Theor. Phys., 7, 183-197 (1973)
[5] Hiscock, WA, Evolution of the interior of a charged black hole, Phys. Lett. A, 83, 3, 110-112 (1981)
[6] Gürsel, Y.; Novikov, ID; Sandberg, VD; Starobinsky, AA, Final state of the evolution of the interior of a charged black hole, Phys. Rev. D, 20, 1260-1270 (1979)
[7] Poisson, E.; Israel, W., Inner-horizon instability and mass inflation in black holes, Phys. Rev. Lett., 63, 1663-1666 (1989)
[8] Poisson, E.; Israel, W., Internal structure of black holes, Phys. Rev. D, 41, 1796-1809 (1990)
[9] Ori, A., Inner structure of a charged black hole: an exact mass-inflation solution, Phys. Rev. Lett., 67, 789-792 (1991) · Zbl 0990.83529
[10] Gnedin, ML; Gnedin, NY, Destruction of the cauchy horizon in the reissner-nordstrom black hole, Class. Quantum Gravity, 10, 6, 1083 (1993)
[11] Brady, PR; Smith, JD, Black hole singularities: a numerical approach, Phys. Rev. Lett., 75, 1256-1259 (1995) · Zbl 1020.83590
[12] Burko, LM, Structure of the black hole‘s Cauchy horizon singularity, Phys. Rev. Lett., 79, 4958-4961 (1997) · Zbl 0953.83021
[13] Hod, S.; Piran, T., Mass inflation in dynamical gravitational collapse of a charged scalar field, Phys. Rev. Lett., 81, 1554-1557 (1998)
[14] Burko, LM; Ori, A., Analytic study of the null singularity inside spherical charged black holes, Phys. Rev., D57, 7084-7088 (1998)
[15] Dafermos, M., Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations, Ann. Math., 158, 3, 875-928 (2003) · Zbl 1055.83002
[16] Dafermos, M., Luk, J.: The interior of dynamical vacuum black holes I: The \(C^0\)-stability of the Kerr Cauchy horizon, arXiv:1710.01722 [gr-qc]
[17] Ori, A., Oscillatory null singularity inside realistic spinning black holes, Phys. Rev. Lett., 83, 5423-5426 (1999) · Zbl 0951.83023
[18] Ori, A., Perturbative approach to the inner structure of a rotating black hole, Gen. Relativ. Gravit., 29, 881-929 (1997) · Zbl 0883.53068
[19] Burko, L.M., Khanna, G., Zenginoǧlu, A.: Cauchy-horizon singularity inside perturbed Kerr black holes. Phys. Rev. D 93(4), 041501 (2016). arXiv:1601.05120 [gr-qc]. [Erratum: Phys. Rev. D 96(12)129903 (2017)]
[20] Dias, OJC; Eperon, FC; Reall, HS; Santos, JE, Strong cosmic censorship in de Sitter space, Phys. Rev., D 97, 10, 104060 (2018)
[21] Chesler, PM; Narayan, R.; Curiel, E., Singularities in Reissner-Nordström black holes, Class. Quant. Grav., 37, 2, 025009 (2020) · Zbl 1478.83140
[22] Chesler, P. M.: Singularities in rotating black holes coupled to a massless scalar field, arXiv:1905.04613 [gr-qc]
[23] Kommemi, J., The Global structure of spherically symmetric charged scalar field spacetimes, Commun. Math. Phys., 323, 35-106 (2013) · Zbl 1275.83002
[24] Luk, J., Oh, S.-J.: Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region, arXiv:1702.05715 [gr-qc] · Zbl 1429.83046
[25] Dafermos, M., Black holes without spacelike singularities, Commun. Math. Phys., 332, 729-757 (2014) · Zbl 1301.83021
[26] Mädler, T.; Winicour, J., Bondi-Sachs Formalism, Scholarpedia, 11, 33528 (2016)
[27] Marolf, D.; Ori, A., Outgoing gravitational shock-wave at the inner horizon: the late-time limit of black hole interiors, Phys. Rev. D, 86, 124026 (2012)
[28] Eilon, E.; Ori, A., Numerical study of the gravitational shock wave inside a spherical charged black hole, Phys. Rev., D 94, 10, 104060 (2016)
[29] Chesler, PM; Curiel, E.; Narayan, R., Numerical evolution of shocks in the interior of Kerr black holes, Phys. Rev., D 99, 8, 084033 (2019)
[30] Burko, L. M., Khanna, G.: Marolf-Ori singularity inside fast spinning black holes. Phys. Rev. D 99, 081501 (2019). doi:10.1103/PhysRevD.99.08150arXiv:1901.03413 [gr-qc]
[31] Dafermos, M.; Rodnianski, I., A Proof of Price‘s law for the collapse of a selfgravitating scalar field, Invent. Math., 162, 381-457 (2005) · Zbl 1088.83008
[32] Donninger, R., Schlag, W. & Soffer, A.: On pointwise decay of linear waves on a Schwarzschild black hole background. Commun. Math. Phys. 309, 51-86 (2012). doi:10.1007/s00220-011-1393-8arXiv:0911.3179 [math.AP] · Zbl 1242.83054
[33] Metcalfe, J., Tataru, D., Tohaneanu, M.: Price’s law on nonstationary space-times. Adv. Math. 230(3), 995-1028 (2012). doi:10.1016/j.aim.2012.03.010. arXiv:1104.5437 [math.AP] · Zbl 1246.83070
[34] Angelopoulos, Y.; Aretakis, S.; Gajic, D., Late-time asymptotics for the wave equation on spherically symmetric, stationary spacetimes, Adv. Math., 323, 529-621 (2018) · Zbl 1381.83051
[35] Chesler, PM; Yaffe, LG, Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes, JHEP, 07, 086 (2014) · Zbl 1421.81111
[36] Belinsky, VA; Khalatnikov, IM; Lifshitz, EM, Oscillatory approach to a singular point in the relativistic cosmology, Adv. Phys., 19, 525-573 (1970)
[37] Belinski, VA; Khalatnikov, IM, Effect of scalar and vector fields on the nature of the cosmological singularity, Sov. Phys. JETP, 36, 591 (1973)
[38] Cardoso, V.; Costa, JL; Destounis, K.; Hintz, P.; Jansen, A., Quasinormal modes and strong cosmic censorship, Phys. Rev. Lett., 120, 3, 031103 (2018)
[39] Hollands, S., Wald, R. M., Zahn, J.: Quantum instability of the Cauchy horizon in Reissner-Nordström-deSitter spacetime. Class. Quantum Grav. 37, 115009 (2020). doi:10.1088/1361-6382/ab8052. arXiv:1912.06047 [gr-qc] · Zbl 1478.83190
[40] Van de Moortel, M.: The breakdown of weak null singularities inside black holes, arXiv:1912.10890 [gr-qc] · Zbl 1462.83009
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.