Chemical Potential and Charge in Quantum Black Holes

TL;DR

This paper uses holography to analyze quantum black holes with defects sourcing electric or magnetic charges, revealing quantum effects on their electromagnetic fields and discovering new classes of extremal charged quantum black holes.

Contribution

It extends holographic solutions to include quantum backreaction of charged defects, leading to novel quantum black hole solutions with improved electromagnetic behavior.

Findings

Quantum electromagnetic fields decay better at infinity than classical ones.

Found new (near-)extremal charged quantum black holes with AdS$_2$ throats.

Quantum effects significantly alter black hole electromagnetic properties.

Abstract

We study systems in $2+1$ dimensions consisting of defects that source an electric charge, or a magnetic flux, of a $U(1)$ field, and we use holography to compute their effects on quantum conformal fields. We can also hide the defects inside the horizon of a black hole, where they continue to affect the quantum fields outside. By extending the solutions to braneworld holography, we find the non-linear backreaction of the quantum fields on the defect and black hole backgrounds. This gives quantum charged point particles and black holes. The charged quantum black holes markedly differ from classically charged BTZ black holes, since the quantum-induced electromagnetic field in $2+1$ dimensions has a better asymptotic behavior than its classical counterpart. The construction also gives a new class of (near-)extremal charged quantum black holes with AdS$_2$ throats.