Lovelock black holes with non-constant curvature horizon

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.

17 pages, Published version

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• Extended phase space thermodynamics for Lovelock black holes with non-maximally symmetric horizons
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• 5D Lovelock gravity: new exact solutions with torsion
• Topologically nontrivial black holes in Lovelock-Born-Infeld gravity
• Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions
• Lovelock Branes
• Exotic Black Hole Thermodynamics in Third-Order Lovelock Gravity
• Geometrical origin of the Kodama vector
• Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity
• Inhomogeneous metrics on complex bundles in Lovelock gravity
• Existence and absence of Killing horizons in static solutions with symmetries
• New solutions of exotic charged black holes and their stability
• Universal $p$-form black holes in generalized theories of gravity
• Negative Mass Black Holes in de-Sitter Space
• Robinson-Trautman solutions with scalar hair and Ricci flow