Radiation from collapsing shells, semiclassical backreaction and black hole formation

TL;DR

This paper analyzes quantum radiation from collapsing shells, showing that backreaction does not prevent black hole formation and providing detailed calculations and conceptual clarifications.

Contribution

It offers an analytically solvable model for collapsing shells, demonstrating thermal radiation emission and clarifying the impact of backreaction on horizon formation.

Findings

Collapsing shells emit approximately thermal radiation near the horizon.

Backreaction effects do not prevent event horizon formation.

Radiation flux delays but does not stop black hole formation.

Abstract

We provide a detailed analysis of quantum field theory around a collapsing shell and discuss several conceptual issues related to the emission of radiation flux and formation of black holes. Explicit calculations are performed using a model for a collapsing shell which turns out to be analytically solvable. We use the insights gained in this model to draw reliable conclusions regarding more realistic models. We first show that any shell of mass $M$ which collapses to a radius close to $r=2M$ will emit approximately thermal radiation for a period of time. In particular, a shell which collapses from some initial radius to a final radius $2M(1-\epsilon^2)^{-1}$ (where $\epsilon \ll 1$) without forming a black hole, will emit thermal radiation during the period $M\lesssim t \lesssim M\ln (1/\epsilon^2)$. Later on ($t\gg M \ln(1/\epsilon^2)$), the flux from such a shell will decay to zero exponentially. We next study the effect of backreaction computed using the vacuum expectation value of the stress tensor on the collapse. We find that, in any realistic collapse scenario, the backreaction effects do \emph{not} prevent the formation of the event horizon. The time at which the event horizon is formed is, of course, delayed due to the radiated flux -- which decreases the mass of the shell -- but this effect is not sufficient to prevent horizon formation. We also clarify several conceptual issues and provide pedagogical details of the calculations in the Appendices to the paper.