Analytic models for gravitational collapse

TL;DR

This paper introduces two analytical models of gravitational collapse leading to Schwarzschild black holes, exploring conditions under which singularities form or are avoided, thus advancing understanding of singularity development in general relativity.

Contribution

The paper presents novel analytical models of gravitational collapse based on a revisited Schwarzschild solution, analyzing singularity formation and avoidance.

Findings

One model forms a singularity immediately after collapse begins.

The other model avoids finite-time singularity formation during collapse.

The models satisfy certain energy conditions under specific collapse rates.

Abstract

We present two analytical models of gravitational collapse toward the Schwarzschild black hole, starting from the interior of the revisited Schwarzschild solution recently reported in [Phys. Rev. D 109, 104032 (2024)]. Both models satisfy some energy conditions at all times as long as the collapse is slower than some limit. While a singularity of the Schwarzschild black hole at the origin ($R_{\mu\nu\alpha\beta}R^{\mu\nu\alpha\beta}\sim r^{-6}$) forms immediately after the start of the collapse in one model, such a singularity never appear at finite time during the collapse (except $t\to\infty$) in the other model. The scheme used shows great potential for studying in detail the appearance of singularities in general relativity.