Deriving The Bekenstein-Hawking entropy by Statistical Mechanics and Quantization of Non-Commuting Space

TL;DR

This paper derives the Bekenstein-Hawking entropy for black holes using statistical mechanics and quantized non-commuting space, and shows that gravity equations emerge from quantum and statistical principles.

Contribution

It introduces a novel approach linking quantized non-commuting space with gravitational and thermodynamic equations, providing a quantum-statistical foundation for gravity.

Findings

Derivation of Bekenstein-Hawking entropy from quantized space

Emergence of Einstein and Newton gravity equations from statistical mechanics

Gravity and thermodynamics equations have quantum and statistical origins

Abstract

In this paper, we derive the Bekenstein-Hawking entropy by considering a Non-Commuting two dimensional quantized space, and we will show that the Bekenstein-Hawking entropy is valid for the system (black hole) in an equilibrium state. Also, by using the entropy was obtained, we derive the Einstein and Newton gravity equation, and finally, we get an equation that is consistent with the previous results. In other words, we want to show that by using the statistical mechanics and quantization of space and the excitation of space quanta, can be obtained the Einstein and Newton gravity equation. In general, we try to show that the all equation of gravity and thermodynamics of gravitational systems have quantum and statistical origin.