Abstract
We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS5 × S5 can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for mathcal{N}=4 super Yang-Mills.
Highlights
Theories [19]1 has no large cancellation between bosons and fermions at large N, it scales like N 3/2 [17, 24, 25] and correctly reproduces the entropy of a class of BPS black holes in AdS4 × S7
Bulgaria E-mail: morteza.hosseini@mib.infn.it, khristov@inrne.bas.bg, alberto.zaffaroni@mib.infn.it Abstract: We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS5 × S5 can be obtained by a simple extremization principle
Where ∆I are chemical potentials conjugated to the electric charges QI and ω1,2 chemical potentials conjugated to the angular momenta Jφ, Jψ
Summary
The change of coordinates t = t, φ = φ − gt, ψ = ψ − gt, and y2 = r2 + 2rm2 /3 transforms the metric to a static frame at infinity. In order to bring the metric into a manifestly asymptotically AdS5 spacetime (in the global sense) as y → ∞ we make the following change of coordinates [5]. The solution has a regular event horizon at rh = 0 only for nonzero angular momenta in AdS5. The angular velocities of the horizon, measured with respect to the azimuthal coordinates ψ and φ of the asymptotically static frame at infinity, are. The Bekenstein-Hawking entropy of the black hole is proportional to its horizon area and can be compactly written in terms of the physical charges as [39]. We will obtain the Bekenstein-Hawking entropy (2.24) of the BPS black hole from an extremization principle
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