De Sitter magnetic black hole dipole with a supersymmetric horizon

TL;DR

This paper presents a new non-BPS solution in N=2 gauged supergravity featuring a symmetric universe with two extremal black holes of opposite magnetic charges, one of which is supersymmetric, with entropy independent of scalar moduli.

Contribution

It introduces a novel non-BPS solution with a supersymmetric horizon in gauged supergravity, expanding understanding of black hole configurations with magnetic charges and scalar field behavior.

Findings

The solution describes a symmetric universe with two extremal black holes and singularities.

One horizon exhibits supersymmetry, the other does not, yet entropy remains constant.

Scalar fields vary at horizons but do not affect the entropy value.

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. At one of the horizon the solution becomes $\frac 12$-BPS supersymmetric, while at the other one there is no supersymmetry, but the entropy remains independent from the scalar modulus.