Non-extremal black holes of N=2, d=4 supergravity

Abstract

We propose a generic recipe for deforming extremal black holes into non-extremal black holes and we use it to find and study the non-extremal black-hole solutions of several N=2,d=4 supergravity models (SL(2,R)/U(1), CPn and STU with four charges). In all the cases considered, the non-extremal family of solutions smoothly interpolates between all the different extremal limits, supersymmetric and not supersymmetric. This fact can be used to find explicitly extremal non-supersymmetric solutions in the cases in which the attractor mechanism does not completely fix the values of the scalars on the event horizon and they still depend on the boundary conditions at spatial infinity. We compare (supersymmetry) Bogomol'nyi bounds with extremality bounds, we find the first-order flow equations for the non-extremal solutions and the corresponding superpotential, which gives in the different extremal limits different superpotentials for extremal black holes. We also compute the "entropies" (areas) of the inner (Cauchy) and outer (event) horizons, finding in all cases that their product gives the square of the moduli-independent entropy of the extremal solution with the same electric and magnetic charges.

Many small, inessential changes. Some misprints corrected and a few references added

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• Black string first order flow in N=2, d=5 abelian gauged supergravity
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• Universality of Area Product: Solutions with Conical Singularity
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• Developments in special geometry
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• Camouflaged Supersymmetry
• Non-perturbative black holes in Type-IIA String Theory vs. the No-Hair conjecture
• The violation of the No-Hair Conjecture in four-dimensional ungauged Supergravity
• $E_{7(7)}$ invariant non-extremal entropy
• Chaotic Dynamics in Extremal Black Holes: A Challenge to the Chaos Bound
• Topological solutions in ungauged Supergravity
• Regular 3-charge 4D black holes and their microscopic description
• New supersymmetric black holes in four dimensional N=2 supergravity
• Instability of Near-Extremal Black Holes in N=2, d=4 Supergravity