Constructing black hole solutions in supergravity theories

Abstract

We perform a detailed analysis of black hole solutions in supergravity models. After a general introduction on black holes in general relativity and supersymmetric theories, we provide a detailed description of ungauged extended supergravities and their dualities. Therefore, we analyze the general form of black hole configurations for these models, their near-horizon behavior and characteristic of the solution. An explicit construction of a black hole solution with its physical implications is given for the STU-model. The second part of this review is dedicated to gauged supergravity theories. We describe a step-by-step gauging procedure involving the embedding tensor formalism, to be used to obtain a gauged model starting from an ungauged one. Finally, we analyze general black hole solutions in gauged models, providing an explicit example for the N = 2, D = 4 case. A brief review on special geometry is also provided, with explicit results and relations for supersymmetric black hole solutions. *(3) -transformation, the group G (3) is broken to the

New non-extremal and BPS hairy black holes in gauged $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 8 supergravity

“…Now we want to study supersymmetryc configurations for our model, namely configurations satisfying eqs. (C.1) [50]. First it is useful to make a change of coordinates that puts metric (3.25e) in the standard form (see appendix B.2)…”

“…The assumption is not generic, since in asymptotically AdS black holes the solutions generating technique[40][41][42][43][44][45][46][47][48][49][50], based on the global isometry group of the ungauged theory, can no longer be applied in a gauged model, due to the non-trivial duality action on the embedding tensor[51,52].…”

Exact holographic RG flows in extended SUGRA

“…The above issue can be avoided using the embedding tensor formulation of the gauging procedure [40][41][42][43][44][45][46][47][48][49][50][51], in which all deformations involved are encoded in a single object, the JHEP04(2021)053 embedding tensor Θ, which is itself covariant with respect to the global symmetries of the ungauged model. This procedure allows to formally restore the symmetries at the level of the (gauged) field equations and Bianchi identities, provided the embedding tensor is transformed together with the other fields.…”

New Black Hole Solutions in N=2 and N=8 Gauged Supergravity

“…Now we want to study supersymmetryc configurations for our model, imposing the vanishing of the SUSY variations [22,36]. First it is useful to make a change of coordinates that puts metric (19c) in the standard form…”