5D Schwarzschild-Like Spacetimes with Arbitrary Magnetic Field

TL;DR

This paper presents a new class of exact five-dimensional Einstein solutions with four-dimensional Schwarzschild-like behavior, incorporating arbitrary magnetic fields and analyzing their singularities and asymptotic properties.

Contribution

It introduces novel five-dimensional solutions with customizable magnetic fields, extending Schwarzschild solutions and analyzing their singularity structures.

Findings

Solutions are asymptotically flat

Singularities depend on magnetic multipole moments

Regularity achieved for monopole fields

Abstract

We find a new class of exact solutions of the five-dimensional Einstein equations whose corresponding four-dimensional spacetime possesses a Schwarzschild-like behavior. The electromagnetic potential depends on a harmonic function and can be choosen to be of a monopole, dipole, etc. field. The solutions are asymptotically flat and for vanishing magnetic field the four metrics are of the Schwarzschild solution. The spacetime is singular in $r=2m$ for higher multipole moments, but regular for monopoles or vanishing magnetic fields in this point. The scalar field posseses a singular behavior. #(Preprint CINVESTAV 15/93)#