Deriving Einstein's Field Equation(EFE) and Modified Gravity by Statistical Mechanics and Quantization of Non-Commuting Space

TL;DR

This paper derives Einstein's field equations and modified gravity from a quantum, non-commutative space framework using statistical mechanics, holography, and the Unruh effect, linking space geometry to energy levels.

Contribution

It introduces a novel derivation of Einstein's equations from non-commutative quantum space and energy-dependent geometry without relying on traditional assumptions.

Findings

Derivation of Einstein's field equations from non-commutative space

Recovery of Newton's law of gravity in the classical limit

Linking space geometry to energy states via holography and Unruh effect

Abstract

In this paper, we derive the Einstein's field equation (EFE) by considering an non-commuting two dimensional quantized space, which can be excited by absorbing energy. Any variation of the energy level of space quantas, will result in a change in the quanta's area state. This means, that the geometry of space depends on the energy which exists in it. Using Holographic principle and Unruh effect, without any further assumptions like equipartition theorem, our model leads to Newton's law of gravity in the limit $\hbar \to 0$.