Hawking radiation as tunneling from a Vaidya black hole in noncommutative gravity

In the context of a noncommutative model of coordinate coherent states, we present a Schwarzschild-like metric for a Vaidya solution instead of the standard Eddington-Finkelstein metric. This leads to the appearance of an exact (t - r) dependent case of the metric. We analyze the resulting metric in three possible causal structures. In this setup, we find a zero remnant mass in the long-time limit, i.e. an instable black hole remnant. We also study the tunneling process across the quantum horizon of such a Vaidya black hole. The tunneling probability including the time-dependent part is obtained by using the tunneling method proposed by Parikh and Wilczek in terms of the noncommutative parameter sigma. After that, we calculate the entropy associated to this noncommutative black hole solution. However, the corrections are fundamentally trifling; one could respect this as a consequence of quantum inspection at the level of semiclassical quantum gravity.