On time evolution of quantum black holes

TL;DR

This paper explores the time evolution of quantum black holes using semiclassical approximation, revealing the potential existence of long-living remnants due to backreaction effects.

Contribution

It introduces a novel approach to incorporate time into quantum black hole evolution by applying semiclassical approximation to the Hamiltonian constraint at the apparent horizon.

Findings

Long-living black hole remnants are suggested when backreaction is included.

The approach bridges quantum gravity equations with Hawking radiation's statistical mechanics.

Results align with microcanonical models of black hole evaporation.

Abstract

The time evolution of black holes involves both the canonical equations of quantum gravity and the statistical mechanics of Hawking radiation, neither of which contains a time variable. In order to introduce the time, we apply the semiclassical approximation to the Hamiltonian constraint on the apparent horizon and show that, when the backreaction is included, it suggests the existence of a long-living remnant, similarly to what is obtained in the microcanonical picture for the Hawking radiation.