Choptuik Scaling and Quantum Effects in 2D Dilaton Gravity

TL;DR

This paper investigates the classical and semiclassical collapse of scalar fields in 2D dilaton gravity, revealing a quantum-induced mass gap at black hole formation threshold that differs from classical scaling behavior.

Contribution

It provides the first numerical analysis of quantum effects on black hole formation in 2D dilaton gravity, showing how quantum corrections alter the classical mass scaling near criticality.

Findings

Classical black hole mass scales with threshold parameter as |p-p*|^{0.53}

Semiclassical analysis shows a non-zero mass gap at threshold due to quantum effects

Quantum effects modify the classical critical behavior of black hole formation.

Abstract

We study numerically the collapse of massless scalar fields in two-dimensional dilaton gravity, both classically and semiclassically. At the classical level, we find that the black hole mass scales at threshold like $M_{\rm bh} \propto |p-p^*|^{\gamma}$, where $\gamma \simeq 0.53$. At the semiclassical level, we find that in general $M_{\rm bh}$ approaches a non-zero constant as $p \rightarrow p^*$. Thus, quantum effects produce a mass gap not present classically at the onset of black hole formation.