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–Kähler 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.
Highlights
There has been a growing interest over the past two decades in black holes in more than four dimensions [1]
Effective descriptions of quantum corrections [2] and lowenergy limits of string theory [3] typically result in higher order terms to be added to the Einstein–Hilbert action, so that various gravity theories beyond general relativity have been the subject of increasing attention
This dramatically enlarges the space of vacuum black hole solutions and permitted horizon geometries for generalized theories of gravity, well beyond the usual case of horizons of constant curvature
Summary
There has been a growing interest over the past two decades in black holes in more than four dimensions [1]. Adding a Gauss–Bonnet [9] or Lovelock [10,11,12] term to the Einstein–Hilbert action places a stringent tensorial constraint on the geometry of h This rules out various known “exotic” Einstein black holes and shows that, generically, h cannot be an arbitrary Einstein space in a gravity theory different from Einstein’s. C (2020) 80:1020 ensures that the corresponding field equations automatically reduce to just two ODEs for the two unknown metric functions A(r ) and B(r ) This dramatically enlarges the space of vacuum black hole solutions and permitted horizon geometries for generalized theories of gravity, well beyond the usual case of horizons of constant curvature. We conclude with a short summary and some additional comments in the last Sect. 7
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