Lovelock black holes with maximally symmetric horizons

We investigate some properties of n(\ge 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C^2 vacuum solutions are classified into four types: (i) Schwarzschild-Tangherlini-type solution; (ii) Nariai-type solution; (iii) special degenerate vacuum solution; (iv) exceptional vacuum solution. The conditions for the realization of the last two solutions are clarified. The Schwarzschild-Tangherlini-type solution is studied in detail. We prove the first law of black-hole thermodynamics and present the expressions for the heat capacity and the free energy.

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