N=2 SUGRA BPS multi-center black holes and freudenthal triple systems

¹ IFT, Dept. of Physics, U. Murcia, Murcia, SPAIN
² Dept. of Physics, Harvard University, USA

^a e-mail: etl@um.es

Published online: 29 May 2015

Abstract

We present a detailed description of N = 2 stationary BPS multicenter black hole solutions for quadratic prepotentials with an arbitrary number of centers and scalar fields making a systematic use of the algebraic properties of the matrix of second derivatives of the prepotential, S, which in this case is a scalar-independent matrix. The anti-involution matrix S can be understood as a Freudenthal duality x̃ = Sx. We show that this duality can be generalized to “Freudenthal transformations” under which the horizon area, ADM mass and intercenter distances scale up leaving constant the scalars at the fixed points. In the special case λ = 1, “S-rotations”, the transformations leave invariant the solution. The standard Freudenthal duality can be written as . We argue that these generalized transformations leave invariant not only the quadratic preotential theories but also the general stringy extremal quartic form Δ₄, Δ₄(x) = Δ₄(cos θx + sin θx̃) and therefore its entropy at lowest order.