Vacuum Non Singular Black Hole in Tetrad Theory of Gravitation

Abstract

The field equations of a special class of tetrad theory of gravitation have been applied to tetrad space having three unknown functions of radial coordinate. The spherically symmetric vacuum stress-energy momentum tensor with one assumption concerning its specific form generates two non-trivial different exact analytic solutions for these field equations. For large $r$, the exact analytic solutions coincide with the Schwarzschild solution, while for small $r$, they behave in a manner similar to the de Sitter solution and describe a spherically symmetric black hole singularity free everywhere. The solutions obtained give rise to two different tetrad structures, but having the same metric, i.e., a static spherically symmetric nonsingular black hole metric. We then, calculated the energy associated with these two exact analytic solutions using the superpotential method. We find that unless the time-space components of the tetrad go to zero faster than $ \displaystyle{1 \over \sqrt{r}}$ at infinity, the two solutions give different results. This fact implies that the time-space components of the tetrad must vanish faster than $\displaystyle{1 \over \sqrt{r}}$ at infinity.