Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry

TL;DR

This paper derives an exact axi-symmetric solution in teleparallel gravity with parameters for mass, charge, rotation, and NUT charge, and analyzes its energy and angular momentum distribution.

Contribution

It presents a new exact solution in tetrad theory of gravitation and computes the associated energy and angular momentum in this framework.

Findings

Energy is shared between interior and exterior regions.

Only the Z component of angular momentum is non-zero.

Provides explicit expressions for energy and angular momentum distribution.

Abstract

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters $M$ (mass), $Q$ (charge), $a$ (rotation) and $L$ (NUT). We then, calculate the total exterior energy using the energy-momentum complex given by M{\o}ller in the framework of Weitzenb$\ddot{o}$ck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only non-vanishing components of the angular momentum is in the Z direction.