Physics of the interior of a spherical, charged black hole with a scalar field

TL;DR

This paper investigates the complex interior structure of charged black holes perturbed by scalar fields using advanced numerical simulations, revealing multiple types of singularities and nonlinear gravitational phenomena.

Contribution

It introduces a new numerical code with adaptive mesh refinement to analyze nonlinear effects and the nature of singularities inside charged black holes with scalar perturbations.

Findings

Existence of multiple null and central singularities inside black holes.

Nonlinear effects like mass inflation and matter squeeze depend on initial conditions.

Physical singularities differ from mathematical singularities in position.

Abstract

We analyse the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in addition to investigation of the properties of the mathematical singularities where some curvature scalars are equal to infinity, we analyse the properties of the physical singularities where the Kretschmann curvature scalar is equal to the planckian value. Using a homogeneous approximation we analyse the properties of the spacetime near a spacelike singularity in spacetimes influenced by different matter contents namely a scalar field, pressureless dust and matter with ultrarelativistic isotropic pressure. We also carry out full nonlinear analyses of the scalar field and geometry of spacetime inside black holes by means of an appropriate numerical code with adaptive mesh refinement capabilities. We use this code to investigate the nonlinear effects of gravitational focusing, mass inflation, matter squeeze, and these effects dependence on the initial boundary conditions. It is demonstrated that the position of the physical singularity inside a black hole is quite different from the positions of the mathematical singularities. In the case of the existence of a strong outgoing flux of the scalar field inside a black hole it is possible to have the existence of two null singularities and one central $r=0$ singularity simultaneously.