# Universal Black Holes

## TL;DR

This paper demonstrates a universal method for constructing static vacuum black hole solutions in various metric theories of gravity, broadening the scope of possible solutions and horizon geometries.

## Contribution

It introduces a generalized ansatz that simplifies the field equations to two ODEs and applies to any theory with a Lagrangian built from the Riemann tensor and derivatives.

## Key findings

- Enlarged space of black hole solutions and horizon geometries.
- Explicit solutions in Gauss-Bonnet, quadratic, and $F(R)$ gravity.
- Reduction of field equations to two ordinary differential equations.

## 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.