Black holes in pure Lovelock gravities

Lovelock gravity is a fascinating extension of general relativity, whose action consists of dimensionally extended Euler densities. Compared to other higher order derivative gravity theories, Lovelock gravity is attractive since it has a lot of remarkable features such as the fact that there are no more than second order derivatives with respect to the metric in its equations of motion, and that the theory is free of ghosts. Recently, in the study of black strings and black branes in Lovelock gravity, a special class of Lovelock gravity is considered, which is named pure Lovelock gravity, where only one Euler density term exists. In this paper we study black hole solutions in the special class of Lovelock gravity and associated thermodynamic properties. Some interesting features are found, which are quite different from the corresponding ones in general relativity.

Figure 1

The metric function $f(r)$ (2.21) versus the radius. The upper curve indicates that both the black hole and cosmological horizons exist, while the lower curve is a naked singularity solution.

Figure 2

The metric function $f(r)$ (2.30) versus the radius. The upper curve for a larger $M$ indicates that this solution has a naked singularity, while there are two black hole horizons for the lower curve.