Quantum Hair, Instantons, and Black Hole Thermodynamics: Some New Results

TL;DR

This paper investigates how quantum instantons influence black hole temperature and electric fields, revealing connections between quantum hair, energy conditions, and topological phases in simplified models.

Contribution

It provides an analytic estimate of quantum hair effects on black hole thermodynamics and links non-classical electric fields to topological phases in lower-dimensional models.

Findings

Quantum instantons affect black hole temperature.

Violations of weak energy condition are explicitly demonstrated.

Connection established between black hole charge and topological phases.

Abstract

We present results obtained by a consideration of the non-classical energy momentum tensor associated with Euclidean Instantons outside the event horizon of black holes. We demonstrate here how this allows an analytic estimate to be made of the effect of discrete quantum hair on the temperature of the black hole, in which the role of violations of the weak energy condition associated with instantons is made explicit, and in which the previous results of Coleman, Preskill, and Wilczek are extended. Last, we demonstrate how the existence of a non-classical electric field outside the event horizon of black holes, uncovered by these authors, can be identified with a well-known effect in the Abelian-Higgs model in two dimensions. In this case, there is a one-to-one connection between the discrete charge of a black hole and a topological phase in two dimensions.