Stability of the vacuum non-singular black hole

The singularity of the black hole solutions obtained before in Møller's theory are studied. It is found that although the two solutions reproduce the same associated metric the asymptotic behavior of the scalars of torsion tensor and basic vector are quite different. The stability of the associated metric of those solutions which is spherically symmetric non-singular black hole is studied using the equations of geodesic deviation. The condition for the stability is obtained. From this condition the stability of the Schwarzschild solution and di Sitter solution can be obtained.