Black Holes without Mass and Entropy in Lovelock Gravity

TL;DR

This paper introduces new higher-dimensional Lovelock gravity black hole solutions with zero mass and entropy, challenging traditional thermodynamic interpretations and extending previous Gauss-Bonnet results.

Contribution

It presents a novel class of black hole solutions in Lovelock gravity with unique thermodynamic properties, including zero mass and entropy, and generalizes earlier Gauss-Bonnet findings.

Findings

Black holes have nonzero temperature but zero mass.

Entropy vanishes for odd m and is a constant for even m, but should be considered zero.

Solutions extend known Gauss-Bonnet black holes to general Lovelock gravity.

Abstract

We present a class of new black hole solutions in $D$-dimensional Lovelock gravity theory. The solutions have a form of direct product $\mathcal{M}^m \times \mathcal{H}^{n}$, where $D=m+n$, $\mathcal{H}^n$ is a negative constant curvature space, and are characterized by two integration constants. When $m=3$ and 4, these solutions reduce to the exact black hole solutions recently found by Maeda and Dadhich in Gauss-Bonnet gravity theory. We study thermodynamics of these black hole solutions. Although these black holes have a nonvanishing Hawking temperature, surprisingly, the mass of these solutions always vanishes. While the entropy also vanishes when $m$ is odd, it is a constant determined by Euler characteristic of $(m-2)$-dimensional cross section of black hole horizon when $m$ is even. We argue that the constant in the entropy should be thrown away. Namely, when $m$ is even, the entropy of these black holes also should vanish. We discuss the implications of these results.