Quantum corrections to critical phenomena in gravitational collapse

TL;DR

This paper explores how quantum effects influence critical phenomena in gravitational collapse, revealing a quantum mass gap under certain conditions and discussing the limitations of semi-classical approximations.

Contribution

It derives the structure of the quantum stress-energy tensor on self-similar backgrounds and extends critical collapse analysis to include quantum perturbations, identifying conditions for a quantum mass gap.

Findings

Existence of a quantum mass gap for classical critical exponent $eta \,\geq\, 0.5$

Semi-classical approximation breaks down for $eta < 0.5$

Generalized the scaling law for black hole mass to include quantum effects

Abstract

We investigate conformally coupled quantum matter fields on spherically symmetric, continuously self-similar backgrounds. By exploiting the symmetry associated with the self-similarity the general structure of the renormalized quantum stress-energy tensor can be derived. As an immediate application we consider a combination of classical, and quantum perturbations about exactly critical collapse. Generalizing the standard argument which explains the scaling law for black hole mass, $M \propto |\eta-\eta^*|^\beta$, we demonstrate the existence of a quantum mass gap when the classical critical exponent satisfies $\beta \geq 0.5$. When $\beta < 0.5$ our argument is inconclusive; the semi-classical approximation breaks down in the spacetime region of interest.