Spherically Symmetric Geometries in f(T) and f(R) Gravitational Theories

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© 2015 Gamal G. L. Nashed. Using the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R = - T - 2∇αTα, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is, T = TαμνSαμν = 0 or (ii) total derivative term, that is, ∇αTα with Tα is the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution for f (T) and f (R) gravitational theories.

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