Thermodynamics of hairy black holes in Lovelock gravity

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 'λ-line' -a line of second order phase transitions -in black hole thermodynamics.

Repulsive Interactions and Universal Properties of Charged Anti–de Sitter Black Hole Microstructures

“…In summary, novel information about black hole microstructures can be obtained from a geometric viewpoint. It would be interesting to apply our approach to other black hole systems with various properties, including angular momentum [19], hair [20][21][22], and acceleration [23,24]. The results will provide us with considerably more detailed information concerning the underlying degrees of freedom giving rise to black hole thermodynamics.…”

Reentrant Phase Transitions and Triple Points of Topological AdS Black Holes in Born-Infeld-Massive Gravity

“…Only Van der Waals-like first-order SBH/LBH phase transition exists in these models. In addition, the RPT and triple points also occur in the higher-dimensional rotating AdS black holes [66,67] and higher-dimensional GaussBonnet AdS black hole [68][69][70]. It would be interesting to extend our discussion to these black holes in Gauss-Bonnet and 3rd-order Lovelock-massive gravity.…”

Entropy increases at linear order in scalar-hairy Lovelock gravity

“…It can be regarded as a natural generalization of Lovelock gravity with a non-minimal coupling scalar field. This theory admits a scalar-hairy black hole solution where the scalar field is nonvanishing and regular outside of the singularity [31][32][33][34].…”

“…Here s is a cross-section of event horizon, γ ab is the induced metric on s, andǫ ab is the binormal to s. Because the scalar field can be nonvanishing, the Wald entropy in this theory should also be corrected by the scalar field even for the stationary black hole cases. The validity of the first law and thermodynamics of this entropy in charged scalar-hairy black holes have been discussed in [34]. However, as mentioned in the introduction, the Wald entropy of the purely Lovelock gravity does not obey the linearized second law and we need to focus on the JM entropy [26][27][28].…”

“…In Ref. [34], the thermodynamics of the stationary black hole in this theory has been investigated. They showed that the Wald entropy satisfies the first law.…”