Numerical evolution of the interior geometry of charged black holes
Paul M. Chesler
备注：
11 pages, 8 figures. v2: Clarifications made to introduction and discussion sections. Added discussion concerning critical spacelike singularity formation. Published version
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 approximation. We also demonstrate that the geometry near $r = 0$ is a scalarized Kasner geometry and compute the associated Kasner exponents.
We wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz [{\it Astrophys. Astron.} {\bf 3} (1982) 325] for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya-Tikekar parameter, $k$, indicating deviation form sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions …
The present work contains a discussion on compact stellar body that is influenced by the effects electromagnetic fields. We have tried to discuss a solution of Einstein-Maxwell field equation with the interpretation of Buchdahl spacetime type function. The interior fluid density and anisotropic pressures have been derived for a charged fluid of compact body which is also continuous with the Reissner-Nordstrom metric exterior solution. We have discussed the singularity free interior anisotropic fluid under electromagnetic influence. The thermodynamics energy conditions and their variation with …
We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.
We analyze the "vacuum" polarization induced by a quantum charged scalar field near the inner horizon of a charged (Reissner-Nordström-de Sitter) black hole in quantum states that start out as regular states near an initial Cauchy surface. Contrary to the outer (i.e. event-) horizon, where polarization effects lead to a discharge, we find that near an inner horizon, the transversal component of the expected current density can have either sign depending on the black hole and field parameters. Thus, the inner horizon can be charged or discharged. But we find that it is always discharged close t…
In this exposition, we seek solutions of the Einstein-Maxwell field equations in the presence of a massive scalar field cast in the Brans-Dicke (BD) formalism which describes charged anisotropic strange stars. The interior spacetime is described by a spherically symmetric static metric of embedding class I. This reduces the problem to a single-generating function of the metric potential which is chosen by appealing to physics based on regularity at each interior point of the stellar interior. The resulting model is subjected to rigorous physical checks based on stability, causality and regular…
We study the interior structure of five dimensional neutral helical black holes in Einstein gravity and charged helical black holes in Einstein-Maxwell gravity. Inside the neutral helical black holes, the systems evolve to a stable spacelike Kasner singularity. The metric field related to the helical deformation strength exhibits oscillation behavior close to the horizon at low temperature and small helical deformation strength. Inside the charged helical black holes, we show that the inner Cauchy horizon can not exist. The systems also evolve from the horizon to a stable Kasner singularity. W…
In this paper, we investigate the internal structure of a charged hairy black hole solution in the non-linear massive gravity. We first consider the impact of various configurations of massive gravity on the condensate operator and then probe the black hole interior dynamics. Like a standard holographic superconductor system, just below the critical temperature, the interior evolves through several distinct epochs, including a collapse of the Einstein-Rosen bridge, Josephson oscillations of the scalar field, and finally a Kasner (or Kasner inversion) cosmology. However, for the large massive g…
The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this purpose, we first write explicitly the Einstein field equations for the interior regular region. We take an electrically charged nonisotropic fluid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure $p_r$ is equal to the negative of energy density $ρ$, $p_r=-ρ$. Then, two solutions for the Einstein equations are bu…
For horizonless spherical stars with uniform charge density, the hoop conjecture was tested based on the interior solution. In this work, we are interested in more general horizonless spherical charged stars. We test hoop conjecture using the exterior solution since all types of interior solutions correspond to the same exterior Reissner-Nordsr$\ddot{o}$m solution. Our analysis shows that the hoop conjecture is violated for very compact stars if we express the conjecture with the total ADM mass. And the hoop conjecture holds if we express the conjecture using the mass in the sphere.
