Flow equations and attractors for black holes in N = 2 U(1) gauged
  supergravity

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Abstract

We investigate the existence of supersymmetric static dyonic black holes with spherical horizon in the context of N= 2 U(1) gauged supergravity in four dimensions. We analyze the conditions for their existence and provide the general first-order flow equations driving the scalar fields and the metric warp factors from the asymptotic AdS4 geometry to the horizon. We work in a general duality-symmetric setup, which allows to describe both electric and magnetic gaugings. We also discuss the attractor mechanism and the issue of moduli (de-)stabilization.

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N=2 Extremal Black Holes

Renata Kallosh, Andrew Strominger, Sergio Ferrara (1995)

It is shown that extremal magnetic black hole solutions of N = 2 supergravity coupled to vector multiplets \(X^\Lambda\) with a generic holomorphic prepotential \(F(X^\Lambda)\) can be described as supersymmetric solitons which interpolate between maximally symmetric limiting solutions at spatial infinity and the horizon. A simple exact solution is found for the special case that the ratios of the \(X^\Lambda\) are real, and it is seen that the logarithm of the conformal factor of the spatial metric equals the Kahler potential on the vector multiplet moduli space. Several examples are discussed in detail.

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Supersymmetry and Attractors

, (2009)

We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the Bertotti-Robinson-type geometry. These results provide an explicit model independent expression for the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropy-area formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge.

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STU Black Holes and String Triality

Wing Wong, Joachim Rahmfeld, Renata Kallosh … (1996)

We find double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F=STU. The area formula is STU-moduli independent and has \({[SL(2,Z)]}^3\) symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8, Z) transformation. The area formula of one theory equals that of the dual theory when expressed in terms of dual charges. We analyse the relation between (STU) black holes to string triality of black holes: (S|TU), (T|US), (U|ST) solutions. In the democratic STU-symmetric version we find that all three S and T and U duality symmetries are non-perturbative and mix electric and magnetic charges.