Spherical Collapse of a Mass-Less Scalar Field With Semi-Classical Corrections

TL;DR

This paper numerically studies the collapse of a scalar field with semi-classical corrections, confirming classical critical phenomena and exploring how quantum effects influence black hole formation and evaporation.

Contribution

It demonstrates the impact of semi-classical quantum effects on scalar field collapse and critical phenomena, extending understanding beyond classical models.

Findings

Classical critical phenomena are preserved when quantum effects are weak.

Quantum evaporation reduces initial amplitude without altering echoing structure.

Semi-classical approximation breaks down for small black hole masses with strong quantum effects.

Abstract

We investigate numerically spherically symmetric collapse of a scalar field in the semi-classical approximation. We first verify that our code reproduces the critical phenomena (the Choptuik effect) in the classical limit and black hole evaporation in the semi classical limit. We then investigate the effect of evaporation on the critical behavior. The introduction of the Planck length by the quantum theory suggests that the classical critical phenomena, which is based on a self similar structure, will disappear. Our results show that when quantum effects are not strong enough, critical behavior is observed. In the intermediate regime, evaporation is equivalent to a decrease of the initial amplitude. It doesn't change the echoing structure of near critical solutions. In the regime where black hole masses are low and the quantum effects are large, the semi classical approximation breaks down and has no physical meaning.