Effect of Snyder-de Sitter Model on the black hole thermodynamics in the context of rainbow gravity

One of the foremost goals of theoretical modern physics is to obtain a reliable theory of quantum gravity. In so doing, new fundamental scales are being proposed. For example, in the Snyder-de Sitter (SdS) model, two scales manifest which relate measurement limits of the position and momentum. In this work, we study the thermodynamic functions of the Schwarzschild black hole in the SdS model within the presence of position independent and dependent gravity's rainbow. Heuristically, we prove the presence of a nonzero lower bound value of the horizon, mass and temperature of the black hole. Then, we present the stability and remnant conditions of the black hole according to the entropy and heat capacity functions.