Axially symmetric solution in Teleparallel Theory of Gravitation

TL;DR

This paper derives an axially symmetric exact solution in teleparallel gravity, simplifies its structure function via coordinate transformations, and explores its properties, including singularities and energy content issues.

Contribution

It introduces a new tetrad form with a factorisable structure function, facilitating analysis of axial solutions in teleparallel gravity.

Findings

The structure function's roots are now straightforward to determine.

The tetrad's singularities are analyzed.

Energy calculation yields a non-physical result.

Abstract

An exact solution has an axial symmetry is obtained in the teleparallel theory of gravitation. The associated metric has the structure function G(xi)=1-xi^2-2mA(xi)^3. The cubic nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad that its associated metric has the structure function in a factorisable form. This new form has the advantage that its roots are now trivial to write down. The singularities of the obtained tetrad are studied. Using another coordinate transformation we get a tetrad that its associated metric gives the Schwarzschild spacetime. Calculate the energy content of this tetrad we get a meaningless result!