Are the singularities stable?
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we have analyzed the general problem of stability of the family of the static spherically symmetric solutions of the standard Einstein-Maxwell model coupled to an extra free massless scalar field. We have obtained the equations for the axial and polar perturbations. The stability against axial perturbations has been proven.
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