Solution of deformed Einstein equations and quantum black holes

Abstract

Recently one and two-parameter deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give a deeper insight to the deformed Einstein equations and consider the solutions of these equations for the extremal quantum black holes. We then represent the implications of the solutions, such that the deformation parameters lead the charged black holes to have a smaller mass than the usual Reissner-Nordstr\"om black holes. This reduction in mass of a usual black hole can be considered as a transition from classical to quantum black hole regime.