Universal p-form black holes in generalized theories of 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–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 $$R^2$$ R 2 , Gauss–Bonnet and (a sector of) Einstein–Horndeski gravity coupled to certain p-form and conformally invariant electrodynamics.

Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions

“…Future work may point at extensions of our investigation beyond Einstein's gravity, still in the context of the electrodynamics of [12]. Some results about static black holes are already available, see [32,41,42,65]. Analyzing the thermodynamics of the obtained solutions and their modifications would also be of considerable interest (cf.…”

“…It is interesting to observe that all the above black hole solutions turn out to be "immune" to some corrections to the gravity part of the action (1), i.e., they coincide with electric [40] and magnetic [32] solutions of certain f (R) gravities. This is no longer true for extensions of (1) to Gauss-Bonnet gravity, however exact solutions thereof are also known in the case of electric [41] and dyonic [32] fields (for Gauss-Bonnet magnetic black holes coupled to different power-like electrodynamics see [42]).…”

“…When Λ and Einstein terms are added to the action, or for more general f (R) theories, this remains true provided the parameters of the theory are suitably fine-tuned [43][44][45]. That this is the case can be traced back to the fact that the Ricci scalar of ( 46) is constant [32,[43][44][45]. Similarly, the same metric also solves Einstein's gravity coupled to a conformal scalar field [46].…”

Robinson-Trautman spacetimes coupled to conformally invariant electrodynamics in higher dimensions

“…Interestingly, thanks to the fact that the Ricci scalar of (2.2) is constant, the above black hole solutions can be easily extended to theories for which the Einstein term in (1.1) is replaced by a generic f (R) scalar -examples have been given in [12,13] (see also [14]). 1 Extensions to Gauss-Bonnet gravity are also known, for which the metric function H is instead modified in a non-trivial way [13,18].…”

Pure Gauss–Bonnet NUT black hole with and without non-central singularity

“…It is non-singular and asymptotically non-flat black hole solution with Kretschmann curvature scalar being finite at r = 0. It, however, admits closed timelike curves [9].When we go to higher dimensions, a spectrum of topology opens up for black hole horizon from spherical to product of spheres, for instance in six dimension, it could be S (4) or S (2) ×S (2) or S (1) ×S (3) [10,11]. Interestingly it turns out that all higher dimensional NUT solutions do not have spherical topology but instead have product of 2-spheres [12][13][14][15][16][17].…”