Exotic Black Hole Thermodynamics in Third-Order Lovelock Gravity

TL;DR

This paper explores the thermodynamics and phase transitions of exotic black holes in third-order Lovelock gravity, revealing novel phenomena like triple points and small-large black hole transitions across different dimensions.

Contribution

It extends black hole thermodynamics to exotic horizon geometries in Lovelock gravity, uncovering new phase behaviors and ruling out certain geometries due to singularities.

Findings

Uncharged 7D black holes show triple point phenomena.

Charged black holes undergo small-large phase transitions.

Exotic horizon geometries are often ruled out by naked singularities.

Abstract

The generalization of Birkhoff's theorem to higher dimensions in Lovelock gravity allows for black hole solutions with horizon geometries of non-constant curvature. We investigate thermodynamic aspects of these `exotic' black hole solutions, with a particular emphasis on their phase transitions. We consider an extended phase space where the cosmological constant acts as a thermodynamic pressure, and examine both uncharged and $U(1)$ charged solutions. In $d=7$, black hole solutions are restricted to having constant-curvature horizon base manifolds. Uncharged $d=7$ black holes possess novel triple point phenomena analogous to those recently uncovered in exotic $d=6$ black holes in Gauss-Bonnet gravity, while their charged counterparts generically undergo small-large black hole phase transitions. In $d=8$, we find that both charged and uncharged black holes exhibit triple point behaviour and small-large black hole transitions. We also show that a wide range of `exotic' horizon geometries can be ruled out due to the appearance of naked singularities.