Thermodynamics of hairy black holes in Lovelock gravity

TL;DR

This paper investigates the thermodynamic behavior of Lovelock black holes with scalar hair, revealing novel phenomena such as virtual triple points and lambda-lines, and clarifies conditions for ghost-free theories.

Contribution

It introduces new thermodynamic features like virtual triple points and lambda-lines in hairy Lovelock black holes, expanding understanding of black hole phase transitions.

Findings

Identification of a one-parameter family of critical points.

Discovery of virtual triple points in black hole thermodynamics.

First example of a lambda-line in black hole phase transitions.

Abstract

We perform a thorough study of the thermodynamic properties of a class of Lovelock black holes with conformal scalar hair arising from coupling of a real scalar field to the dimensionally extended Euler densities. We study the linearized equations of motion of the theory and describe constraints under which the theory is free from ghosts/tachyons. We then consider, within the context of black hole chemistry, the thermodynamics of the hairy black holes in the Gauss-Bonnet and cubic Lovelock theories. We clarify the connection between isolated critical points and thermodynamic singularities, finding a one parameter family of these critical points which occur for well-defined thermodynamic parameters. We also report on a number of novel results, including `virtual triple points' and the first example of a `$\lambda$-line'---a line of second order phase transitions---in black hole thermodynamics.