Black hole evaporation based upon a q-deformation description

Abstract

A toy model based upon the $q$-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the spacetime noncommutativity in the vicinity of black hole horizon. We use a trick that all the spacetime noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative spacetime, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cut-off of the spectrum is the prediction of the model.