Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

We calculate the Komar energy E for a noncommutative inspired Schwarzschild black hole. A deformation from the conventional identity E = 2STH is found in the next to leading order computation in the noncommutative parameter θ (i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{O}(\sqrt{\theta}e^{-M^2/\theta})}$$\end{document}) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result M = 2STH, where the mass (M) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter–Schwarzschild geometry.