Universal Black Holes

Abstract

We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct $d$-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed from the Riemann tensor and its covariant derivatives of arbitrary order. Namely, we show that, apart from containing two arbitrary functions $a(r)$ and $f(r)$ (essentially, the $g_{tt}$ and $g_{rr}$ components), in any such theory the line-element may admit as a base space {\em any} isotropy-irreducible homogeneous space. Technically, this ensures that the field equations generically reduce to two ODEs for $a(r)$ and $f(r)$, and dramatically enlarges the space of black hole solutions and permitted horizon geometries for the considered theories. We then exemplify our results in concrete contexts by constructing solutions in particular theories such as Gauss-Bonnet, quadratic, $F(R)$ and $F$(Lovelock) gravity, and certain conformal gravities.

20 pages. v2: abstract, introduction (sec. 1) and final discussion (sec. 9) improved, a few comments and refs. added, appendix B extended (with field eqs. for quadratic gravity). Results unchanged

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Cited by in corpus (8)

• Regular black holes in three dimensions
• Exploring the black hole spectrum of axionic Horndeski theory
• Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions
• Exotic Black Hole Thermodynamics in Third-Order Lovelock Gravity
• Pure Gauss-Bonnet NUT Black Hole Solution: I
• Universal $p$-form black holes in generalized theories of gravity
• New look at AdS black holes with conformal scalar hair
• Pure Gauss-Bonnet NUT black hole with and without non-central singularity