Special Vinberg Cones and the Entropy of BPS Extremal Black Holes

Abstract

We consider the static, spherically symmetric and asymptotically flat BPS extremal black holes in ungauged N = 2 D = 4 supergravity theories, in which the scalar manifold of the vector multiplets is homogeneous. By a result of Shmakova on the BPS attractor equations, the entropy of this kind of black holes can be expressed only in terms of their electric and magnetic charges, provided that the inverse of a certain quadratic map (uniquely determined by the prepotential of the theory) is given. This inverse was previously known just for the cases in which the scalar manifold of the theory is a homogeneous symmetric space. In this paper we use Vinberg's theory of homogeneous cones to determine an explicit expression for such an inverse, under the assumption that the scalar manifold is homogeneous, but not necessarily symmetric. As immediate consequence, we get a formula for the entropy of BPS black holes that holds in any model of N = 2 supergravity with homogeneous scalar manifold.

arXiv comment38 pages; v4: this version is the same of v3; only these comments are modified to announce that a detailed description of the correction of the computational error of v2 -- now fixed in v3 and in this version v4 - can be found in "Erratum to: Special Vinberg Cones and the Entropy of BPS Extremal Black Holes", published in JHEP 06 (2023) 192

References in corpus (14)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• The Dynamics of General Relativity
• N=2 Extremal Black Holes
• Supersymmetry and Attractors
• Black Holes and Critical Points in Moduli Space
• Universality of Sypersymmetric Attractors
• N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
• Special geometry, cubic polynomials and homogeneous quaternionic spaces
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
• Supersymmetric Black Holes
• Erice Lectures on Black Holes and Attractors
• Topics in Cubic Special Geometry
• Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion

Cited by in corpus (1)

• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion