Multidimensional Reissner-Nordstrom Problem with a Generalized Maxwell Field

TL;DR

This paper derives and analyzes static, spherically symmetric solutions in higher-dimensional Einstein-generalized Maxwell systems, revealing new black-hole solutions with unique temperature behaviors and naked singularities.

Contribution

It introduces a generalized Maxwell field preserving conformal invariance in higher dimensions and explores the properties of resulting black-hole solutions, including temperature behavior.

Findings

Most solutions have naked singularities.

Some solutions form black holes with calculable Hawking temperature.

Hawking temperature can grow infinitely in extreme cases.

Abstract

We obtain and study static, spherically symmetric solutions for the Einstein - generalized Maxwell field system in 2n dimensions, with possible inclusion of a massless scalar field. The generalization preserves the conformal invariance of the Maxwell field in higher dimensions. Almost all solutions exhibit naked singularities, but there are some classes of black-hole solutions. For these cases the Hawking temperature is found and its charge/mass and dimension dependence is discussed. It is shown that, unlike the previously known multidimensional black-hole solutions, in our case the Hawking temperature may infinitely grow in the extreme case (that of minimum mass for given charges).