Lovelock black holes with non-constant curvature horizon

TL;DR

This paper explores higher-dimensional Lovelock gravity solutions with non-constant curvature horizons, deriving conditions for Einstein spaces, presenting exact solutions, and analyzing black hole dynamics using a quasilocal mass concept.

Contribution

It introduces algebraic conditions for Einstein spaces in Lovelock gravity, constructs a quasilocal mass, and applies it to study dynamical black holes and Birkhoff's theorem.

Findings

Derived algebraic conditions for Einstein spaces in Lovelock gravity.

Constructed a quasilocal mass satisfying the unified first law.

Analyzed black hole dynamics with trapping horizons.

Abstract

This paper studies a class of $D=n+2(\ge 6)$ dimensional solutions to Lovelock gravity that is described by the warped product of a two-dimensional Lorentzian metric and an $n$-dimensional Einstein space. Assuming that the angular part of the stress-energy tensor is proportional to the Einstein metric, it turns out that the Weyl curvature of an Einstein space must obey two kinds of algebraic conditions. We present some exact solutions satisfying these conditions. We further define the quasilocal mass corresponding to the Misner-Sharp mass in general relativity. It is found that the quasilocal mass is constructed out of the Kodama flux and satisfies the unified first law and the monotonicity property under the dominant energy condition. Making use of the quasilocal mass, we show Birkhoff's theorem and address various aspects of dynamical black holes characterized by trapping horizons.