Charged Axially Symmetric Solution, Energy and Angular Momentum in Tetrad Theory of Gravitation

TL;DR

This paper derives a charged axially symmetric solution in tetrad gravity, calculates its energy and angular momentum distributions using M{\

Contribution

It presents a new charged axially symmetric solution in tetrad theory and evaluates its energy and angular momentum using M{\

Findings

Total energy matches previous results for the interior.

Exterior energy is zero when charge parameter is zero.

Angular momentum is absent in the exterior for zero charge.

Abstract

Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by three parameters ``$ $the gravitational mass $M$, the charge parameter $Q$ and the rotation parameter $a$". The parallel vector fields and the electromagnetic vector potential are axially symmetric. We calculate the total exterior energy. The energy-momentum complex given by M{\o}ller in the framework of the Weitzenb$\ddot{o}$ck geometry ``$ ${\it characterized by vanishing the curvature tensor constructed from the connection of this geometry}" has been used. This energy-momentum complex is considered as a better definition for calculation of energy and momentum than those of general relativity theory. The energy contained in a sphere is found to be consistent with pervious results which is shared by its interior and exterior. Switching off the charge parameter, one finds that no energy is shared by the exterior of the charged axially symmetric solution. The components of the momentum density are also calculated and used to evaluate the angular momentum distribution. We found no angular momentum contributes to the exterior of the charged axially symmetric solution if zero charge parameter is used.