Black holes without mass and entropy in Lovelock gravity

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 the solutions 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 an 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.