Entropic corrections to Newton's law

TL;DR

This paper investigates how entropic corrections to the area-entropy relation influence Newton's law of gravitation, connecting quantum effects and galactic anomalies within Verlinde's emergent gravity framework.

Contribution

It provides a detailed analysis of entropic corrections to gravity, deriving modified Newtonian laws and linking them to quantum effects and galactic rotation anomalies.

Findings

Log corrections produce deviations similar to quantum gravity effects.

Volume corrections resemble modified gravity models for galaxy rotation.

The analysis supports the thermodynamic interpretation of gravity.

Abstract

It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde has proposed a model for gravity with a simple statistical mechanical interpretation that is applicable in the non-relatvistic regime. After critically analyzing the construction, we present a strong consistency check of the model. Specifically, we consider two well-motivated corrections to the area-entropy relation, the log correction and the volume correction, and follow Verlinde's construction to derive corrections to Newton's law of gravitation. We show that the deviations from Newton's law stemming from the log correction have the same form as the lowest order quantum effects of perturbative quantum gravity, and the deviations stemming from the volume correction have the same form as some modified Newtonian gravity models designed to explain the anomalous galactic rotation curves.