Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes

TL;DR

This paper investigates conditions under which static or stationary Einstein-Maxwell black holes with non-inheriting electromagnetic fields cannot exist, providing new nonexistence results under specific assumptions.

Contribution

It establishes nonexistence theorems for static and stationary Einstein-Maxwell black holes with non-inheriting fields under certain conditions.

Findings

Static degenerate black holes are impossible.

Static non-degenerate or stationary black holes are also non-existent under stronger assumptions.

Possible solutions exist if stronger assumptions are relaxed.

Abstract

We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein-Maxwell space-times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to stronger assumptions, nor are static, non-degenerate or stationary black holes. We describe the possibilities if the stronger assumptions are relaxed.