Universal $p$-form black holes in generalized theories of gravity

TL;DR

This paper develops a universal framework for constructing static black hole solutions with $p$-forms in various gravity theories, allowing for more general horizon geometries beyond constant curvature spaces.

Contribution

It introduces a generalized Schwarzschild-like ansatz with isotropy-irreducible homogeneous base spaces, enabling the construction of diverse $p$-form black holes in multiple gravity theories.

Findings

Constructed magnetic and dyonic 2-form solutions in various theories.

Extended black hole solutions to non-constant curvature horizon geometries.

Applied framework to specific theories like $R^2$, Gauss-Bonnet, and Einstein-Horndeski gravity.

Abstract

We explore how far one can go in constructing $d$-dimensional static black holes coupled to $p$-form and scalar fields before actually specifying the gravity and electrodynamics theory one wants to solve. At the same time, we study to what extent one can enlarge the space of black hole solutions by allowing for horizon geometries more general than spaces of constant curvature. We prove that a generalized Schwarzschild-like ansatz with an arbitrary isotropy-irreducible homogeneous base space (IHS) provides an answer to both questions, up to naturally adapting the gauge fields to the spacetime geometry. In particular, an IHS-K\"ahler base space enables one to construct magnetic and dyonic 2-form solutions in a large class of theories, including non-minimally couplings. We exemplify our results by constructing simple solutions to particular theories such as $R^2$, Gauss-Bonnet and (a sector of) Einstein-Horndeski gravity coupled to certain $p$-form and conformally invariant electrodynamics.