Quasi - Regular Modulus Of Vacuum Singular Point Black Hole

Black hole is one of the greatest predictions in general relativity. However,there exist lots of enigmatical physical phenomena related to it and the most well known one is the presence of the central singularity. Physical laws would not work at the central singularity. On the other hand, black hole solution with a central singularity is unavoidable for Einstein’s general relativity. The problem of understanding how avoidance of singularities may be possible in general relativity goes beyond formal importance. Some quantum or geometric models have been suggested to avoid the singularity. In this thesis, we only discuss a kind of geometric model, which is similar to the well studied Bardeen black hole.In order to understand the nature of black hole, we usually use the behavior of the perturbed black hole spacetime which may give a glimpse of what is hidden in the horizon. By perturbing the horizon something inside the black hole might run out,including the quasi-normal modes(QNM) about which we are concerned here. From QNM, we can analyze the stability of the perturbation of black hole spacetime. The complex-valued quasi-normal frequencies encode the information on how a black hole cools down after it has been poked, which are depend on the nature of black hole and on the type of the perturbations.In this thesis, we investigate quasi-normal modes of a spherically symmetric black hole with de Sitter centre due to scalar perturbations. Far away from the black hole, the metric approaches asymptotically to the one of Schwarzschild black hole, while, the metric is asymptotically de Sitter near the center of the black hole. By using 6-order WKB approximation,we analyze the QNM for different values of the metric parameter(it is related to cosmological constant),spherical harmonic index, overtune and the mass of black hole. According to calculations, we ?nd that with the change of the value of, there exist maximum and minimum values of the QNMs and it is worthy to attention that the QNMs have extreme values with a changing overtune for some values of. Analysing the QNM of vacuum nonsingular black hole, which is an exact analytic solution of the Einstein equations that is uncharged and is not relevant to electrodynamics or other theories, will contribute to understand the property of uncharged nonsingular black hole.