Spherically Symmetric Solution in (1+4)‎-Dimensional f ( T )‎ Gravity Theories

Abstract EN

A nondiagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate r plus an angle Φ , which is a generalization of the azimuthal angle ϕ , is applied to the field equations of (1+4)-dimensional f ( T ) gravity theory.

A special vacuum solution with one constant of integration is derived.

The physical meaning of this constant is shown to be related to the gravitational mass of the system and the associated metric represents Schwarzschild in (1+4)-dimension.

The scalar torsion related to this solution vanishes.

We put the derived solution in a matrix form and rewrite it as a product of three matrices: the first represents a rotation while the second represents an inertia and the third matrix is the diagonal square root of Schwarzschild spacetime in (1+4)-dimension.