Phase transitions near black hole horizons

TL;DR

This paper explores phase transitions near black hole horizons, showing how introducing a scalar field leads to new stable black hole solutions with higher entropy, indicating a form of black hole hair formation.

Contribution

It demonstrates that adding a massive scalar field with non-renormalizable interactions induces stable hairy black holes with greater entropy, expanding understanding of black hole phase transitions.

Findings

Stable hairy black holes exist with higher entropy than Reissner-Nordstrom solutions.

Scalar field condenses near the horizon in new solutions.

Conditions for black hole hair formation are characterized.

Abstract

The Reissner-Nordstrom black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field. New stable black hole solutions then exist with greater entropy for fixed mass and charge than the Reissner-Nordstrom solution. In these new solutions, the scalar condenses to a non-zero value near the horizon. Various generalizations of these hairy black holes are discussed, and an attempt is made to characterize when black hole hair can occur.