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Interior Dynamics of Regular Schwarzschild Black Holes

J. Ovalle

TL;DR

The paper addresses the interior dynamics of regular Schwarzschild black holes in a purely geometric setting that avoids extra charges and does not depend on a particular gravitational theory. It identifies an infinite family of regular interior geometries described by a mass function $m(r)$, parameterized by exponents $n_i>2$, yielding a single inner horizon and, for large $n_i$, a full de Sitter core; the exterior horizon remains Schwarzschild with surface gravity $\kappa=1/(2 h)$. By promoting $m(r)$ to a time-dependent function $m(v,r)$ in ingoing EF coordinates, the authors derive dynamical constraints—chiefly a non-crossing ordering of the $n_i(v)$—that govern collapse versus expansion and determine when singularities form beyond the inner horizon. They propose a concrete geometric regularization mechanism, using saturating transitions of $n_i(v)$, to model the formation of a regular BH and the transition from extremal to regular interiors, linking the results to cosmic censorship and singularity resolution. The framework opens a path toward understanding the stringent geometric conditions needed to realize regular BHs and suggests extensions to rotating collapse to test robustness.

Abstract

We present an exact, purely geometric account of the interior dynamics of Schwarzschild black holes, formulated without invoking any specific gravitational theory and free of additional charges beyond the total mass ${\cal M}$. We show that dynamical evolution generically produces new singularities, absent in the static case, whose resolution imposes highly restrictive conditions on gravitational collapse.

Interior Dynamics of Regular Schwarzschild Black Holes

TL;DR

The paper addresses the interior dynamics of regular Schwarzschild black holes in a purely geometric setting that avoids extra charges and does not depend on a particular gravitational theory. It identifies an infinite family of regular interior geometries described by a mass function , parameterized by exponents , yielding a single inner horizon and, for large , a full de Sitter core; the exterior horizon remains Schwarzschild with surface gravity . By promoting to a time-dependent function in ingoing EF coordinates, the authors derive dynamical constraints—chiefly a non-crossing ordering of the —that govern collapse versus expansion and determine when singularities form beyond the inner horizon. They propose a concrete geometric regularization mechanism, using saturating transitions of , to model the formation of a regular BH and the transition from extremal to regular interiors, linking the results to cosmic censorship and singularity resolution. The framework opens a path toward understanding the stringent geometric conditions needed to realize regular BHs and suggests extensions to rotating collapse to test robustness.

Abstract

We present an exact, purely geometric account of the interior dynamics of Schwarzschild black holes, formulated without invoking any specific gravitational theory and free of additional charges beyond the total mass . We show that dynamical evolution generically produces new singularities, absent in the static case, whose resolution imposes highly restrictive conditions on gravitational collapse.

Paper Structure

This paper contains 5 sections, 27 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Regular Schwarzschild BHs.
  3. The dynamic interior.
  4. Extremal $\leftrightarrow$ regular black holes
  5. Singularity resolution and final remarks.

Figures (2)

  • Figure 1: Evolution of the inner horizon $h_{\rm c}(v)$ for the dynamical interior \ref{['minfi-v']}: Collapse for $\dot{n}_i<0$ and expansion for $\dot{n}_i>0$. Horizon $h=2{\cal M}\neq\,h(v)$. Distance $r$ in units of ${\cal M}$.
  • Figure 2: Kretschmann $K(v,r)$ from a quasi extremal to a regular BH for $N=2$ in \ref{['Mr']}, where $n(v)$ is given by \ref{['n2(t)']} with $\alpha=62$, $\beta=3$ and $l(v)=1+n(v)$. There is a maximum just below the horizon: $K(-\infty,h-\delta)\sim(\alpha^2/h^5)\delta$, with $\delta\ll\,1.$ We take $\omega=0.1$.