Vacuum nonsingular black hole in tetrad theory of gravitation

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The field equations of a special class of tetrad theory of gravitation have been applied to a tetrad space having three unknown functions of the radial coordinate. The spherically symmetric vacuum stress-energy momentum tensor with one assumption concerning its specific form generates two nontrivial 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 1/√r at infinity, the two solutions give different results. This fact implies that the time-space components of the tetrad must vanish faster than 1/√r at infinity.

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