Resisting collapse: How matter inside a black hole can withstand gravity

TL;DR

This paper explores how matter inside a black hole can resist gravitational collapse by employing negative radial pressure, challenging classical bounds and suggesting models involving quantum effects and string theory.

Contribution

It reexamines the Buchdahl bound, highlighting the role of negative radial pressure in avoiding collapse, and connects classical and quantum perspectives in black hole modeling.

Findings

Negative radial pressure can prevent collapse within classical GR.

Quantum physics can turn negative pressure into positive pressure.

String theory models support the existence of non-collapsing black hole states.

Abstract

How can a Schwarzschild-sized matter system avoid a fate of gravitational collapse? To address this question, we critically reexamine the arguments that led to the "Buchdahl bound", which implies that the minimal size of a stable, compact object must be larger than nine eighths of its own Schwarzschild radius. Following Mazur and Mottola, and in line with other counterexamples to the singularity theorems, we identify large negative radial pressure extending to the gravitational radius as the essential ingredient for evading the Buchdahl bound. Our results are novel although consistent with many other investigations of models of non-singular black holes. It is shown in particular that a large negative pressure in the framework of classical GR translates into a large positive pressure once quantum physics is incorporated. In this way, a Schwarzschild-sized bound state of closed, interacting fundamental strings in its high-temperature Hagedorn phase can appear to have negative pressure and thus the ability to resist gravitational collapse.