Evaporation of four-dimensional dynamical black holes sourced by the quantum trace anomaly

TL;DR

This paper investigates the quantum-induced evaporation process of four-dimensional black holes formed by gravitational collapse, emphasizing the role of trace anomaly and negative energy flux in the evaporation mechanism.

Contribution

It demonstrates how quantum trace anomaly induces negative energy flux at the horizon, leading to black hole evaporation in a dynamical setting, with explicit calculations in Vaidya spacetime.

Findings

Negative energy flux is linked to quantum trace anomaly outside the horizon.

Black hole evaporation rate can be computed using semiclassical Einstein equations.

Evaporation is driven by ingoing negative energy flux associated with quantum matter.

Abstract

We study the evaporation of a four-dimensional spherically symmetric black hole formed in a gravitational collapse. We analyze the back-reaction of a massless quantum scalar field conformally coupled to the scalar curvature by means of the semiclassical Einstein equations. We show that the evaporation is linked to an ingoing negative energy flux at the dynamical horizon and that this flux is induced by the quantum matter trace anomaly outside the black hole horizon whenever a suitable averaged energy condition is satisfied. For illustrative purposes, we evaluate the negative ingoing flux and the corresponding rate of evaporation in the case of a null radiating star described by the Vaidya spacetime.