Abstract
We present a new family of asymptotically locally hbox {AdS}_5 squashed supersymmetric black hole solutions of Fayet–Iliopoulos gauged {{{mathcal {N}}}}=2, D=5 supergravity with two vector multiplets that have a natural uplift to type IIB supergravity. Our new family of black holes is characterized by three parameters, of which two control the horizon geometry while the latter regulates the squashing at the boundary. We evaluate the main physical properties of the family of solutions using holographic renormalization and find that the entropy is independent on the squashing and it is reproduced by using the angular momentum and the Page charges. In previously known solutions Page and holographic charges are equal, due to the vanishing of the Chern–Simons term that here, instead, is relevant. This result suggests that for asymptotically locally hbox {AdS}_5 solutions we should refer to the Page charges to describe the thermodynamics of the system.
Highlights
The same problem in one lower dimension has been solved four years ago starting in [20]
We present a new family of asymptotically locally AdS5 squashed supersymmetric black hole solutions of Fayet–Iliopoulos gauged N = 2, D = 5 supergravity with two vector multiplets that have a natural uplift to type IIB supergravity
In the present paper we have constructed a new family of supersymmetric asymptotically locally AdS5 (AlAdS5) black holes with a boundary geometry containing a squashed S3
Summary
We briefly review the main features of the fivedimensional N = 2 Fayet–Iliopoulos gauged supergravity we consider in this paper. The bosonic sector of the theory is composed of the metric gμν, by nV +1 Abelian gauge fields AμI and by nV real scalar fields I. For convenience it is customary to parametrize the latter using nV + 1 real fields X I which fulfill the constraint. The constraint (2.1) can more be written by introducing lower-index scalars X I defined as XI. In the bosonic sector the main consequence of this gauging is the introduction of the following scalar potential:. The bosonic action of the theory in mostly-plus signature is. From the action (2.7) it is possible to derive the Einstein, Maxwell and scalar equations [15], Rμν − Q I J FμIρ FνJ ρ − Q I J ∇μ X I ∇ν X J
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