EPJ Web of Conferences 95, 04068 (2015)
https://doi.org/10.1051/epjconf/20159504068

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” $$x\to \lambda \exp \left(\theta S\right)x=ax+b\tilde{x}$$ 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 $$\tilde{x}=\text{exp }\left(\frac{\pi }{2}S\right)x$$. 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.