Black Hole Motion in Entropic Reformulation of General Relativity

TL;DR

This paper explores modeling black hole motion using an entropic action based on horizon areas, showing consistency with Newtonian mechanics but highlighting the need to refine dimensionless parameters for accurate physical predictions.

Contribution

It introduces an entropic action approach for black hole dynamics and demonstrates its consistency with classical mechanics, emphasizing the importance of correct dimensionless coefficients.

Findings

Entropic action based on horizon areas aligns with Newton's laws.

Dimensionless coefficients differ from unity, requiring refinement.

Highlights the importance of accurate parameter values in entropic gravity models.

Abstract

We consider a system of black holes -- a simplest substitute of a system of point particles in the mechanics of general relativity -- and try to describe their motion with the help of entropic action: a sum of the areas of black hole horizons. We demonstrate that such description is indeed consistent with the Newton's laws of motion and gravity, modulo numerical coefficients, which coincide but seem different from unity. Since a large part of the modern discussion of entropic reformulation of general relativity is actually based on dimensional considerations, for making a next step it is crucially important to modify the argument, so that these dimensionless parameters acquire correct values.