Static pure Lovelock black hole solutions with horizon topology ${\mathbf{S}}^{(\mathbf{n})}\times {\mathbf{S}}^{(\mathbf{n})}$

Abstract

It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order $N$ for topology ${\mathbf{S}}^{(\mathbf{n})}\times {\mathbf{S}}^{(\mathbf{n})}$. We thus obtain pure Lovelock static black hole solutions with two-sphere topology for any order $N$, and in particular we study in full detail the third and fourth order Lovelock black holes. It is remarkable that thermodynamical stability of black hole discerns between odd and even $N$, and consequently between negative and positive $\Lambda$ and it favours the former while rejecting the latter.

21 pages. Matches JHEP published version

References in corpus (2)

• Lovelock black holes with maximally symmetric horizons
• Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory

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