Black Holes without Mass and Entropy in 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.

V2, Revtex4, 27 pages, no figures, some details and references added, to be published in Phys.Rev.D