Hawking radiation in k-spacetime

Abstract

In this paper, we analyze the Hawking radiation of a k-deformed-Schwarzschild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the k-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzschild metric obtained in the k-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1+1 dimensions to solve the k-deformed Klein-Gordon equation in the background of the Schwarzschild metric. The method of Bogoliubov coefficients is then used to calculate the thermal spectrum of k-deformed-Schwarzschild black hole and show that the Hawking temperature is modified by the noncommutativity of the k-spacetime.