Higher Dimensional Cylindrical or Kasner Type Electrovacuum Solutions

TL;DR

This paper explores higher-dimensional Kasner-type electrovacuum solutions, revealing new solution classes, analyzing their properties, and comparing them with known four-dimensional counterparts in cylindrical and cosmological contexts.

Contribution

It introduces four novel higher-dimensional electrovacuum solutions, including one without a four-dimensional equivalent, and examines their properties and differences from lower-dimensional cases.

Findings

Four new solution types identified, one unique to higher dimensions.

Differences in solution ranges compared to four-dimensional cases.

Connection to Bonnor-Melvin magnetic universe for specific parameters.

Abstract

We consider a D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resembles the same form with four dimensional one, there is a difference on the range of the solutions for fixed signs of the parameters. General magnetic field vacuum solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic universe for a special choice of the parameters. The Kasner forms of the general solution are also presented for the cylindrical or cosmological cases.