Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity

TL;DR

This paper investigates anti-de Sitter black holes in higher curvature gravity theories, analyzing thermodynamic properties, phase transitions, and holographic relations, revealing new conditions for Hawking-Page transitions and entropy relations.

Contribution

It extends the analysis of AdS black holes to Einstein-Gauss-Bonnet and R^2 gravity, identifying new phase transition conditions and entropy relations in these theories.

Findings

Hawking-Page transition occurs for negative curvature horizons with higher curvature terms.

Finite coupling effects can trigger phase transitions for N>5.

Entropy relations are established between bulk and boundary data, with approximate calculations for R^2 terms.

Abstract

We study anti-de Sitter black holes in the Einstein-Gauss-Bonnet and the generic R^2 gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page type thermal phase transitions in these theories. In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature (k=1). But, with the Gauss-Bonnet or/and the (Riemann)^2 interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature (k=-1). We examine the finite coupling effects, and find that N>5 could trigger a Hawking-Page phase transition in the latter theory. For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on first law and Noether charge. With (Riemann)^2 term, however, we can do this only approximately, and the two results agree when, r_H>>L, the size of the horizon is much bigger than the AdS curvature scale. We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry. Following a heuristic approach, we estimate the difference between Hubble entropy {\cal S}_H and Bekenstein-Hawking entropy {\cal S}_{BH} with (Riemann)^2 term, which, for k=0 and k=-1, would imply {\cal S}_{BH}\leq {\cal S}_H.