Existence of Static Dyonic Black Holes in $4d$ $N = 1$ Supergravity With Finite Energy

TL;DR

This paper proves the existence and uniqueness of static dyonic black hole solutions in four-dimensional N=1 supergravity with specific near-horizon and asymptotic geometries, including scalar field interpolation.

Contribution

It establishes the first rigorous proof of unique static dyonic black hole solutions in 4D N=1 supergravity with prescribed geometric conditions.

Findings

Existence of unique solutions for scalar fields interpolating near-horizon and asymptotic regions.

Characterization of near-horizon geometry as a product of two Einstein surfaces.

Asymptotic geometry with constant scalar curvature.

Abstract

We prove the existence and the uniqueness of the static dyonic black holes in four dimensional $N=1$ supergravity theory coupled vector and scalar multiplets. We set the near-horizon geometry to be a product of two Einstein surfaces, whereas the asymptotic geometry has to be a space of constant scalar curvature. Using these data, we show that there exist a unique solution for scalar fields which interpolates these regions.