Galli, P., Ortin, T., Perz, J., & Shahbazi, C. S. (2011). Non-extremal black holes of N=2, d=4 supergravity. J. High Energy Phys., 07(7), 041.
Abstract: We propose a generic recipe for deforming extremal black holes into nonextremal black holes and we use it to find and study the static non-extremal black-hole solutions of several N = 2, d = 4 supergravity models (SL(2, R)/U(1), (CP) over bar (n) 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 explicitly find extremal non-supersymmetric solutions also 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.
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Galli, P., Ortin, T., Perz, J., & Shahbazi, C. S. (2012). From supersymmetric to non-supersymmetric black holes. Fortschritte Phys.-Prog. Phys., 60(9-10), 1026–1029.
Abstract: Methods similar to those used for obtaining supersymmetric black hole solutions can be employed to find also non-supersymmetric solutions. We briefly review some of them, with the emphasis on the non-extremal deformation ansatz of [1].
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Galli, P., Meessen, P., & Ortin, T. (2013). The Freudenthal gauge symmetry of the black holes of N=2, d=4 supergravity. J. High Energy Phys., 05(5), 011–15pp.
Abstract: We show that the representation of black-hole solutions in terms of the variables H-M which are harmonic functions in the supersymmetric case is non-unique due to the existence of a local symmetry in the effective action. This symmetry is a continuous (and local) generalization of the discrete Freudenthal transformations initially introduced for the black-hole charges and can be used to rewrite the physical fields of a solution in terms of entirely different-looking functions.
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Bueno, P., Galli, P., Meessen, P., & Ortin, T. (2013). Black holes and equivariant charge vectors in N=2, d=4 supergravity. J. High Energy Phys., 09(9), 010–51pp.
Abstract: We extend previous investigations on the construction of extremal supersymmetric and non-supersymmetric solutions in the H-FGK formalism to unconventional solutions with anharmonic terms. We show how the use of fake charge vectors equivariant under duality transformations simplifies and clarifies the task of identification of the attractors of the theory.
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Galli, P., Goldstein, K., Katmadas, S., & Perz, J. (2011). First-order flows and stabilisation equations for non-BPS extremal black holes. J. High Energy Phys., 06(6), 070–28pp.
Abstract: We derive a generalised form of flow equations for extremal static and rotating non-BPS black holes in four-dimensional ungauged N = 2 supergravity coupled to vector multiplets. For particular charge vectors, we give stabilisation equations for the scalars, analogous to the BPS case, describing full known solutions. Based on this, we propose a generic ansatz for the stabilisation equations, which surprisingly includes ratios of harmonic functions.
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