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We apply the H-FGK formalism to the study of some properties of the general class of black holes in N=2 supergravity in four dimensions that correspond to the harmonic and hyperbolic ansatze and 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., Comment: Latex2e file +Bibtex file, 35 pages, no figures

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., Comment: 7 pages

We study general classes and properties of extremal and non-extremal static black-hole solutions of N=2, d=5 supergravity coupled to vector multiplets using the recently proposed H-FGK formalism, which we also extend to static black strings. We explain how to determine the integration constants and physical parameters of the black-hole and black-string solutions. We derive some model-independent statements, including the transformation of non-extremal flow equations to the form of those for the extremal flow. We apply our methods to the construction of example solutions (among others a new extremal string solution of heterotic string theory on K_3 \times S^1). In the cases where we have calculated it explicitly, the product of areas of the inner and outer horizon of a non-extremal solution coincides with the square of the moduli-independent area of the horizon of the extremal solution with the same charges., Comment: 33 pages. Revised version: references added. No other changes

We rewrite the Ferrara-Gibbons-Kallosh (FGK) black-hole effective action of N=2, d=4,5 supergravities coupled to vector multiplets, replacing the metric warp factor and the physical scalars with real variables that transform in the same way as the charges under duality transformations, which simplifies the equations of motion. For a given model, the form of the solution in these variables is the same for all spherically symmetric black holes, regardless of supersymmetry or extremality., Comment: 10 pages; v2: references added, some editing of the text, results unchanged; v3: references added as in the published version

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

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., Comment: 27 pages; v2: presentation improved and references added as in the published version

Using the superpotential approach we generalize Denef's method of deriving and solving first-order equations describing multicenter extremal black holes in four-dimensional N = 2 supergravity to allow non-supersymmetric solutions. We illustrate the general results with an explicit example of the stu model., Comment: 17 pages, v2: some clarifications added

For both extremal and non-extremal spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity, we derive a general form of first-order gradient flow equations, equivalent to the equations of motion. For theories that have a symmetric moduli space after a dimensional reduction over the timelike direction, we discuss the condition for such a gradient flow to exist. This note reviews the results of arXiv:0810.1528 [hep-th]., Comment: 6 pages, contribution to the proceedings of the 4th RTN Workshop 'Constituents, Fundamental Forces and Symmetries of the Universe', Varna, 11-17 September 2008; v2: a reference added

We derive a general form of first-order flow equations for extremal and non-extremal, static, spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity. By rewriting the action as a sum of squares a la Bogomol'nyi, we identify the function governing the first-order gradient flow, the `generalised superpotential', which reduces to the `fake superpotential' for non-supersymmetric extremal black holes and to the central charge for supersymmetric black holes. For theories whose scalar manifold is a symmetric space after a timelike dimensional reduction, we present the condition for the existence of a generalised superpotential. We provide examples to illustrate the formalism in four and five spacetime dimensions., Comment: 27 pages, v2: small changes, referencing and misprints corrected, v3: text updated and a reference added to match the JHEP version

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N=2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five- and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions., Comment: 21 pages. v2: Summary section added

We use the relation between extremal black hole solutions in five- and in four-dimensional N=2 supergravity theories with cubic prepotentials to define the entropy function for extremal black holes with one angular momentum in five dimensions. We construct two types of solutions to the associated attractor equations., Comment: 15 pages, minor changes

At the horizon, a static extremal black hole solution in N=2 supergravity in four dimensions is determined by a set of so-called attractor equations which, in the absence of higher-curvature interactions, can be derived as extremization conditions for the black hole potential or, equivalently, for the entropy function. We contrast both methods by explicitly solving the attractor equations for a one-modulus prepotential associated with the conifold. We find that near the conifold point, the non-supersymmetric solution has a substantially different behavior than the supersymmetric solution. We analyze the stability of the solutions and the extrema of the resulting entropy as a function of the modulus. For the non-BPS solution the region of attractivity and the maximum of the entropy do not coincide with the conifold point., Comment: 19 pages, 4 figures, AMS-LaTeX, reference added

Within the context of the entropic principle, we consider the entropy of supersymmetric black holes in N=2 supergravity theories in four dimensions with higher-curvature interactions, and we discuss its maximization at points in moduli space at which an excess of hypermultiplets becomes massless. We find that the gravitational coupling function F^(1) enhances the maximization at these points in moduli space. In principle, this enhancement may be modified by the contribution from higher F^(g)-couplings. We show that this is indeed the case for the resolved conifold by resorting to the non-perturbative expression for the topological free energy., Comment: 22 pages, 8 figures, AMS-LaTeX