De sitter magnetic black hole dipole with a supersymmetric horizon

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 1/2-BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus.

Automated summary

This study presents a new non BPS solution in N = 2 D = 4 gauged supergravity theory, which exhibits perfectly symmetric geometry and satisfies the attractor mechanism.