Noncommutative inspired Schwarzschild black hole, Voros product and Komar energy

The importance of the Voros product in defining a noncommutative Schwarzschild black hole is shown. The entropy is then computed and the area law is shown to hold upto order (1)/√θe-M2/θ. 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 deformation from the conventional identity E = 2STH is found at the order √θe-M2/θ. This deformation leads to a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. Finally, the Smarr formula is worked out. Similar features also exist for a deSitter–Schwarzschild geometry.