Thermodynamic studies of the rainbow gravity-inspired higher-dimensional Schwarzschild black hole: Snyder–de Sitter model

Abstract

One of the staple objectives of theoretical physics is to establish a reliable theory of quantum gravity. To achieve this goal, some fundamental scales are proposed in the modern era, e.g. two scales are proposed in the Snyder–de Sitter model. These two scales relate to measurement limits of the position and momentum. In this paper, we study the thermodynamic properties of the higher-dimensional Schwarzschild black hole in the context of rainbow gravity in the Snyder–de Sitter model within the presence and absence of rainbow gravity and compare our results for [Formula: see text] with the results which are already derived in the previous literature [B. Hamil and B. C. Lütfüoğlu, Int. J. Geom. Methods Mod. Phys. 19, 2250047 (2022)]. We find the existence of the remnant temperature of the concerned black hole. Unlike the four-dimensional Schwarzschild black hole, the black hole in higher dimensions [Formula: see text] has two remnant temperatures. Moreover, we observe that in the rainbow gravity background a nonzero lower bound value of the temperature of the black hole exists. Finally, we analyze the thermal stability remnant conditions of the black hole by computing the heat capacity within this model.