Phase transitions in charged topological black holes dressed with a scalar hair

TL;DR

This paper investigates phase transitions in charged topological black holes with scalar hair within Einstein-Maxwell theory, revealing both second-order and first-order transitions influenced by temperature and scalar self-interaction strength.

Contribution

It identifies and characterizes two distinct phase transitions in hairy black holes, including the conditions under which scalar hair forms or disappears, depending on temperature and coupling constants.

Findings

Second-order phase transition at a specific temperature.

First-order phase transition depending on scalar coupling constant.

Scalar hair formation occurs below a critical temperature.

Abstract

Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black is thermodynamically favored. However, when the temperature exceeds the critical value a hairy black hole is likely to be occur.