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.