De sitter magnetic black hole dipole with a supersymmetric horizon

Abstract

We find a new non BPS solution in N = 2 D = 4 gauged supergravity coupled to U(1) gauge fields and matter. It consists in a closed universe with two extremal black holes of equal size, surrounding two singularities. They have opposite magnetic charges (and no electric charges), but stay in static equilibrium thanks to the positive pressure of a cosmological constant. The geometry is perfectly symmetric under the exchange of the black holes and the flip of the sign of the charges. However the scalar field is non constant and non symmetric, with different values at the horizons, which depend on a real modulus. Remarkably we show that it satisfies the attractor mechanism and the entropy indeed depends only on the magnetic charges. At one of the horizons the solution becomes $$ \frac{1}{2} $$ 1 2 -BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus.

Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification

“…In gauged supergravity, the physical scenarios open up to a wide range of possibilities, one of which will be the object of the present investigation. Recent years witnessed unanticipated progress in finding BPS, as well as non-BPS and non-extremal, thermal BH solutions in generally matter coupled N = 2 gauged supergravity in D = 4 space-time dimensions; see for instance [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In presence of gauging (of the isometries of the scalar manifolds), the supersymmetric BH solutions may be asymptotically AdS 4 and preserve all eight supersymmetries, with the scalars being fixed at critical points (at least local minima) of the gauge potential itself.…”