Entropy quantization of Schwarzschild–de Sitter black hole

The canonical formalism of a spherically symmetric spacetime has been decomposition with respect to the radial coordinate r in the context of 3+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 + 1$$\end{document} split of spacetime. We have set up an effective Lagrangian that plays the role of independent variable couple with metric function. The surface gravity of Schwarzschild–de Sitter black hole has been quantized from the test particle moving around different energy states like Bohr’s atomic model. We have quantized the Hawking temperature and entropy of Schwarzschild–de Sitter black hole from quantization of surface gravity. We also have shown that the change of entropy reduced to zero when the boundary shrinks to very small size.