Einstein Equations and MOND Theory from Debye Entropic Gravity

TL;DR

This paper derives modified Einstein and Poisson equations, as well as MOND theory, from a Debye entropic gravity framework, addressing low-temperature effects and providing a thermodynamic origin for MOND.

Contribution

It introduces a Debye model-based modification to entropic gravity, offering a new thermodynamic perspective on Einstein equations and MOND theory.

Findings

Modified Einstein and Poisson equations derived from Debye entropic gravity.

MOND theory can be understood within the Debye entropic gravity framework.

Results reduce to standard gravity equations at high temperatures.

Abstract

Verlinde's proposal on the entropic origin of gravity is based strongly on the assumption that the equipartition law of energy holds on the holographic screen induced by the mass distribution of the system. However, from the theory of statistical mechanics we know that the equipartition law of energy does not hold in the limit of very low temperature. Inspired by the Debye model for the equipartition law of energy in statistical thermodynamics and adopting the viewpoint that gravitational systems can be regarded as a thermodynamical system, we modify Einstein field equations. We also perform the study for Poisson equation and modified Newtonian dynamics (MOND). Interestingly enough, we find that the origin of the MOND theory can be understood from Debye entropic gravity perspective. Thus our study may fill in the gap existing in the literature understanding the theoretical origin of MOND theory. In the limit of high temperature our results reduce to their respective standard gravitational equations.