Energy equipartition and minimal radius in entropic gravity

TL;DR

This paper examines the limitations of energy equipartition in entropic gravity models, revealing that finite energy bounds lead to significant deviations from Newtonian gravity and suggest a connection to black hole horizons.

Contribution

It demonstrates that assuming finite maximum energy in microscopic systems causes corrections to Newton's law and predicts a singularity at a finite radius, impacting entropic gravity theories.

Findings

Equipartition fails for systems with bounded energy.

Finite energy bounds lead to modifications in gravitational acceleration.

A singularity appears at a finite radius, related to black hole horizons.

Abstract

In this article, we investigate the assumption of equipartition of energy in arguments for the entropic nature of gravity. It has already been pointed out by other authors that equipartition is not valid for low temperatures. Here we additionally point out that it is similarly not valid for systems with bounded energy. Many explanations for black hole entropy suggest that the microscopic systems responsible have a finite dimensional state space, and thus finite maximum energy. Assuming this to be the case leads to drastic corrections to Newton's law for high gravitational fields, and, in particular, to a singularity in acceleration at finite radius away from a point mass. This is suggestive of the physics at the Schwarzschild radius. We show, however, that the location of the singularity scales differently.