Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity

TL;DR

This paper explores how the Snyder-de Sitter model influences black hole thermodynamics within rainbow gravity, revealing lower bounds on black hole parameters and conditions for stability and remnants.

Contribution

It introduces the effects of the Snyder-de Sitter quantum gravity model on Schwarzschild black hole thermodynamics in rainbow gravity, highlighting new bounds and stability conditions.

Findings

Existence of non-zero lower bounds for black hole horizon, mass, and temperature.

Conditions for black hole stability based on entropy and heat capacity.

Implications for black hole remnants in quantum gravity models.

Abstract

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 model, two scales manifest which relate measurement limits of the position and momentum. In this work, we study the thermodynamic functions of the Scharwzschild black hole in the Snyder - de Sitter model within the presence of position-independent and dependent gravity's rainbow. Heuristically, we prove the presence of a non-zero 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.