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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., 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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