Special Vinberg cones and the entropy of BPS extremal black holes

• Published in: The journal of high energy physics Vol. 2021; no. 11; pp. 100 - 35
• Main Authors: Alekseevsky, Dmitri V., Marrani, Alessio, Spiro, Andrea
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 15.11.2021; Springer Nature B.V; SpringerOpen
• Subjects: Black Holes; Classical and Quantum Gravitation; Classical Theories of Gravity; Cones; Differential and Algebraic Geometry; Elementary Particles; Geometry; High energy physics; Manifolds; Physics; Physics and Astronomy; Polynomials; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supergravity; Supergravity Models; Classical Theories of Gravity; Differential and Algebraic Geometry; Supergravity Models; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2021)100

A bstract 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.