Electromagnetic Field in Higher-Dimensional Black-Hole Spacetimes

TL;DR

This paper constructs a special electromagnetic field in higher-dimensional rotating black hole spacetimes, revealing its relation to hidden symmetries and generalizing four-dimensional charged black hole fields, though gravitational back reaction remains unresolved.

Contribution

It introduces a new electromagnetic field aligned with hidden symmetries in higher-dimensional black holes, extending known four-dimensional solutions.

Findings

Electromagnetic field aligned with principal Killing-Yano tensor.

Generalization of four-dimensional charged black hole fields.

Back reaction of the electromagnetic field cannot be solved in higher dimensions.

Abstract

A special test electromagnetic field in the spacetime of the higher-dimensional generally rotating NUT-(A)dS black hole is found. It is adjusted to the hidden symmetries of the background represented by the principal Killing-Yano tensor. Such electromagnetic field generalizes the field of charged black hole in four dimensions. In higher dimensions, however, the gravitational back reaction of such a field cannot be consistently solved.