In this study, we consider three independent physical studies and try to combine them to find an interesting result. Ubriaco’s q-deformed bosons and Verlinde’s entropic gravity studies are taken into account to find the deformed Einstein equations for describing the gravitational field of deformed objects, such as, Strominger’s black holes obeying the deformed Bose or Fermi statistics. We consider the gravitation as an entropic force, as in Verlinde’s approach and assume the source of gravitation is the q-deformed bosons of Ubriaco. Consequently, we obtain the deformed Einstein equations for these deformed bosons by considering the gravitation as an entropic force.
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-Nordström black holes. This reduction in mass of a usual black hole can be considered as a transition from classical to quantum black hole regime.
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