Exact Axially Symmetric Solution in f(T) Gravity Theory

Abstract

A general tetrad field with sixteen unknown functions is applied to the field equations of f(T) gravity theory. An analytic vacuum solution is derived with two constants of integration and an angle Φ that depends on the angle coordinate ϕ and radial coordinate r. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.