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 of f(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.
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Notes
We use the Latin indices i,j,… for local holonomic spacetime coordinates and the Greek indices α,β,… for the (co)frame components.
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Acknowledgements
This work is partially supported by the Egyptian Ministry of Scientific Research under project No. 24-2-12.
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Nashed, G.G.L. A spherically symmetric null tetrads in non-minimal torsion-matter coupling extension of f(T) gravity. Astrophys Space Sci 357, 157 (2015). https://doi.org/10.1007/s10509-015-2385-5
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DOI: https://doi.org/10.1007/s10509-015-2385-5