A spherically symmetric null tetrads in non-minimal torsion-matter coupling extension of f(T) gravity

Abstract

We construct a null tetrad from a non-diagonal spherically symmetric vierbein field, involving two unknown functions of radial coordinate r. This null tetrad is applied to the equations of motion of non-minimal torsion-matter coupling extension off(T) gravity. Exact vacuum solution with two constants of integration is obtained. The scalar torsion related to this special solution is constant. The energy of this solution is calculated using the Euclidean continuation method and the known value is derived. We also calculate the thermodynamical quantities of charged Schwarzschild spacetime and investigate the validity of the first law of thermodynamics and quantum statistical relation.