Thermodynamic Instability of Black Holes of Third Order Lovelock Gravity

TL;DR

This paper investigates the thermodynamic stability of third order Lovelock black holes, revealing an intermediate unstable phase in certain conditions, which differs from lower order theories and depends on parameters and dimensions.

Contribution

It provides the first detailed stability analysis of uncharged third order Lovelock black holes, highlighting the existence of unstable phases not present in lower order theories.

Findings

Unstable phase exists for hyperbolic horizon black holes.

Stability depends on Lovelock coefficients and dimensions.

Higher dimensions can exhibit unstable phases in black holes.

Abstract

In this paper, we compute the mass and the temperature of the uncharged black holes of third order Lovelock gravity and compute the entropy through the use of first law of thermodynamics. We perform a stability analysis by studying the curves of temperature versus the mass parameter, and find that there exists an intermediate thermodynamically unstable phase for black holes with hyperbolic horizon. The existence of this unstable phase for the uncharged topological black holes of third order Lovelock gravity does not occur in the lower order Lovelock gravity. We also perform a stability analysis for a spherical, 7-dimensional black hole of Lovelock gravity and find that while these kinds of black holes for small values of Lovelock coefficients have an intermediate unstable phase, they are stable for large values of Lovelock coefficients. We also find that there exists an intermediate unstable phase for these black holes in higher dimensions. This stability analysis shows that the thermodynamic stability of black holes with curved horizons is not a robust feature of all the generalized theories of gravity.