Behavior of a Chiral Condensate Around Astrophysical-Mass Schwarschild and Reissner-Nordstr\"om Black Holes

TL;DR

This paper introduces a perturbative approach to analyze the behavior of a chiral condensate around astrophysical black holes, validating it against numerical results and exploring effects of charge and extremality on symmetry restoration.

Contribution

It develops and tests a perturbative method for studying chiral condensates around realistic black holes, including charged cases, revealing how black hole properties influence symmetry restoration.

Findings

Perturbative method agrees with previous numerical results.

Size of chiral symmetry restoration bubble scales with black hole size.

Charge-to-mass ratio affects the extent of symmetry restoration, especially near extremality.

Abstract

In this work, we develop a perturbative method to describe the behavior of a chiral condensate around a spherical black hole whose mass is astrophysically realistic. We use the inverse mass as the expansion parameter for our perturbative series. We test this perturbative method in the case of a Schwarzschild black hole, and we find that it agrees well with previous numerical results. For an astrophysical-mass Schwarzschild black hole, the leading order contribution to the condensate is much larger (in most of space) than the next-to-leading order contribution, providing further evidence for the validity of the perturbative approach. The size of the bubble of restored chiral symmetry is directly proportional to the size of the black hole. Next, we apply this perturbative method to a Reissner-Nordstr\"om (RN) black hole. We find that, as the charge-to-mass ratio increases, the bubble of restored chiral symmetry becomes larger relative to the black hole. This effect is particularly pronounced for near-extremal RN black holes. The case of an extremal RN black hole provides an interesting counterexample to the standard thermal explanation for the formation of a bubble of restored chiral symmetry around a black hole.