Black holes in Sol minore
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Springer
Received: September 24, Revised: November 8, Accepted: November 27, Published: December 23,
2019 2019 2019 2019
Black holes in Sol minore
a
Dipartimento di Fisica, Universit` a di Milano, Via Celoria 16, I-20133 Milano, Italy b INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy
E-mail: [email protected], [email protected], [email protected] Abstract: We consider black holes in five-dimensional N = 2 U(1)-gauged supergravity coupled to vector multiplets, with horizons that are homogeneous but not isotropic. We write down the equations of motion for electric and magnetic ans¨atze, and solve them explicitely for the case of pure gauged supergravity with magnetic U(1) field strength and Sol horizon. The thermodynamics of the resulting solution, which exhibits anisotropic scaling, is discussed. If the horizon is compactified, the geometry approaches asymptotically a torus bundle over AdS3 . Furthermore, we prove a no-go theorem that states the nonexistence of supersymmetric, static, Sol-invariant, electrically or magnetically charged solutions with spatial cross-sections modelled on solvegeometry. Finally, we study the attractor mechanism for extremal static non-BPS black holes with nil- or solvegeometry horizons. It turns out that there are no such attractors for purely electric field strengths, while in the magnetic case there are attractor geometries, where the values of the scalar fields on the horizon are computed by extremization of an effective potential Veff , which contains the charges as well as the scalar potential of the gauged supergravity theory. The entropy density of the extremal black hole is then given by the value of Veff in the extremum. Keywords: AdS-CFT Correspondence, Black Holes, Classical Theories of Gravity, Supergravity Models ArXiv ePrint: 1908.07421
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP12(2019)151
JHEP12(2019)151
Federico Faedo,a,b Daniele Angelo Farottia and Silke Klemma,b
Contents 1
2 N = 2, D = 5 U(1)-gauged supergravity
3
3 Equations of motion for electric and magnetic ans¨ atze 3.1 Electric ansatz 3.2 Magnetic ansatz
4 4 5
4 Magnetic black hole in pure gauged supergravity
6
5 Existence of static, Sol-invariant BPS solutions 5.1 Electric ansatz 5.2 Magnetic ansatz
8 9 11
6 Attractor mechanism 6.1 Magnetic ansatz 6.2 Electric ansatz
15 16 17
A Homogeneous manifolds
18
1
Introduction and summary of results
In the seventies of the last century Hawking proved his famous theorem [1, 2] on the topology of black holes, which asserts that event horizon cross sections of 4-dimensional asymptotically flat stationary black holes obeying the dominant energy condition are topologically S2 . This result extends to outer apparent horizons in black hole spacetimes that are not necessarily stationary [3]. Such restrictive uniqueness theorems do not hold in higher dimensions, the most famous counterexample being the black ring of Emparan and Reall [4], with horizon topology S2 × S
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