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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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Galli, P., Goldstein, K., & Perz, J. (2013). On anharmonic stabilisation equations for black holes. J. High Energy Phys., 03(3), 036–7pp.
Abstract: We investigate the stabilisation equations for sufficiently general, yet regular, extremal (supersymmetric and non-supersymmetric) and non-extremal black holes in four-dimensional N = 2 supergravity using both the H-FGK approach and a generalisation of Denef's formalism. By an explicit calculation we demonstrate that the equations necessarily contain an anharmonic part, even in the static, spherically symmetric and asymptotically flat case.
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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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Galli, P., Ortin, T., Perz, J., & Shahbazi, C. S. (2013). Black-hole solutions of N=2, d=4 supergravity with a quantum correction, in the H-FGK formalism. J. High Energy Phys., 04(4), 157–37pp.
Abstract: We apply the H-FGK formalism to the study of some properties of a general class of black holes in N = 2 supergravity in four dimensions that correspond to the harmonic and hyperbolic ansatze and we obtain explicit extremal and non-extremal solutions for the t(3) model with and without a quantum correction. Not all solutions of the corrected model (quantum black holes), including in particular a solution with a single q(1) charge, have a regular classical limit.
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