Quantum corrections to critical phenomena in gravitational collapse

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, $M \propto |η-η^*|^β$, we demonstrate the existence of a quantum mass gap when the classical critical exponent satisfies $β\geq 0.5$. When $β< 0.5$ our argument is inconclusive; the semi-classical approximation breaks down in the spacetime region of interest.