Anomaly induced quantum correction to charged black holes; geometry and thermodynamics

TL;DR

This paper studies quantum corrections to charged black holes caused by energy-momentum trace anomaly, revealing significant effects on geometry, thermodynamics, and stability, especially for small and near-extremal black holes, with implications for dark matter.

Contribution

It introduces quantum-induced corrections to charged black hole properties, including geometry and thermodynamics, highlighting the stability of small black holes and their potential as dark matter candidates.

Findings

Logarithmic correction to black hole entropy.

Lower mass limit for black holes at zero charge.

Small black holes can remain in thermal equilibrium without volume constraints.

Abstract

We consider the corrections due to quantum fluctuations of fields on charged black holes induced from the energy-momentum trace anomaly. Although the number of horizons stays unchanged and their positions receive only finite corrections, the geometry, thermodynamics and formation of RN black holes change seriously in particular for small ones. The entropy receives a logarithmic correction. The line $Q=M$, separating naked singularities from physical solutions is corrected, putting a lower limit on the mass and an upper limit on the temperature of the black hole as a function of its charge. The modifications are highly significant in the cases of near-extremal and small black holes. We also show that for black holes with small mass can stay in thermal equilibrium without any constraint on the volume of the container. This result is in contrast to the large black holes that need a finite volume container for thermal equilibrium. The minimum of the mass lower limits occurs at zero charge, resulting in the extremal Schwarzschild black hole with a specific mass of the order of $M_{p}$ and zero temperature. This state which has only gravitational interaction will be the final stage of Hawking radiation. Stability and lack of any interaction but gravitational, makes the extremal Schwarzschild black hole a serious candidate for dark matter particle.