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

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 $\hbar \to 0$.