Cylindrically Symmetric Solution in Teleparallel Theory of Gravitation

TL;DR

This paper derives an exact cylindrically symmetric solution in teleparallel gravity with electromagnetic fields, revealing how magnetic parameters influence spacetime energy content and reducing to flat spacetime when the magnetic field is zero.

Contribution

It presents a new exact analytic solution in teleparallel gravity with cylindrical symmetry and electromagnetic fields, expanding understanding of energy distribution in such spacetimes.

Findings

Solution characterized by a constant magnetic field parameter B_0

Energy content differs from previous results

Reduces to flat spacetime when B_0=0

Abstract

The field equations of a special class of teleparallel theory of gravitation and electromagnetic fields have been applied to tetrad space having cylindrical symmetry with four unknown functions of radial coordinate $r$ and azimuth angle $\theta$. The vacuum stress-energy momentum tensor with one assumption concerning its specific form generates one non-trivial exact analytic solution. This solution is characterized by a constant magnetic field parameter $B_0$. If $B_0=0$ then, the solution will reduces to the flat spacetime. The energy content is calculated using the superpotential given in the framework of teleparallel geometry. The energy contained in a sphere is found to be different from the pervious results.