Voros product and noncommutative inspired black holes

Abstract: We emphasize the importance of the Voros product in defining noncommutative inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordstr\"{o}m black holes show that the area law holds upto order $\frac{1}{\sqrt{\theta}}e^{-M^2/\theta}$. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy $E$ for these black holes is then obtained and a deviation from the standard identity $E=2ST_H$ is found at the order $\sqrt{\theta}e^{-M^2/\theta}$. This deviation leads to a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. The Smarr formula is finally worked out for the noncommutative Schwarzschild black hole. Similar features also exist for a deSitter--Schwarzschild geometry.