Uniqueness of dark matter magnetized static black hole spacetime

TL;DR

This paper investigates the uniqueness of static axially symmetric black hole solutions in a magnetic universe with dark matter, showing that under certain conditions, the solution is a Schwarzschild-like black hole immersed in a dark matter Melvin universe.

Contribution

It demonstrates the uniqueness of static axially symmetric black hole solutions in Einstein-Maxwell-dark photon gravity with dark matter, extending the black hole uniqueness theorems to include dark matter effects.

Findings

Solutions are uniquely characterized as Schwarzschild-like black holes in dark matter Melvin universe.

All solutions with given boundary and regularity conditions are of the same form.

The dark photon interacts with Maxwell fields via kinetic mixing, influencing black hole solutions.

Abstract

Uniqueness problem of static axially symmetric black hole in magnetic Universe filled with {\it dark matter} component has been considered. The {\it dark matter} model comprises the additional $U(1)$-gauge field ({\it dark photon}) interacting with Maxwell one by the kinetic mixing term. We show that all the solutions of Einstein-Maxwell {\it dark photon} gravity subject to the same boundary and regularity conditions authorize the only static axially symmetric black hole solutions with non-vanishing time and azimuthal components of Maxwell and {\it hidden} sector gauge fields, say Schwarzschild-like black hole immersed in {\it dark matter} Melvin Universe.