Perturbed black holes

Abstract

The first exact solution of Einstein's gravitational field equations that is considered, is the static, spherically symmetric Schwarzschild solution, which describes the gravitational field around a spherical ball of matter. By examining the singularities of this solution, the formation of the Schwarzschild black hole is studied by considering a collapsing ball of dust. The Schwarzschild solution is expressed in Weyl form and then perturbed by the inclusion of a static, axisymmetric weak gravitational field in the external region of the original isolated black hole, such that a Schwarzschild local black hole is obtained. This local black hole is then extended by using the Kruskal-Szekeres extension, in such a way that it is asymptotically fiat at null infinity. The result of this extension is a true perturbed Schwarzschild black hole. A particular class of perturbed Schwarzschild black holes is obtained by taking a special type of the external gravitational field. Another exact solution of Einstein's equations that is derived is the C-metric solution, which is also static and axisymmetric. This represents approximately the field around a uniformly accelerated black hole. Again after expressing this solution in Weyl form, it is perturbed as in the Schwarzschild case by the inclusion of a static, axisymmetric gravitational field in the external region of the black hole, such that a C-metric local black hole is obtained whose extension is called a perturbed C-metric black hole. By considering a specific external gravitational field, an example of a perturbed C-metric black hole is obtained.