A special exact spherically symmetric solution in f(T) gravity theories

A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate r, is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is obtained. The scalar torsion related to this special solution vanishes. To understand the physical meaning of the constant of integration we calculate the energy associated with this solution and show how it is related to the gravitational mass of the system. © 2013 Springer Science+Business Media New York.