English

Universal Black Holes

General Relativity and Quantum Cosmology 2020-02-20 v2 High Energy Physics - Theory

Abstract

We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct dd-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)a(r) and f(r)f(r) (essentially, the gttg_{tt} and grrg_{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)a(r) and f(r)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)F(R) and FF(Lovelock) gravity, and certain conformal gravities.

Keywords

Cite

@article{arxiv.1907.08788,
  title  = {Universal Black Holes},
  author = {Sigbjørn Hervik and Marcello Ortaggio},
  journal= {arXiv preprint arXiv:1907.08788},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T10:25:54.099Z