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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=TμναSαμν=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

advances in high energy physics

Spherically Symmetric Geometries in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>Gravitational Theories

Spherically Symmetric Geometries inf(T)andf(R)Gravitational Theories