Entropic force law in the presence of a noncommutative inspired spacetime for a solar system scale

TL;DR

This paper explores how a noncommutative inspired spacetime affects entropic force laws at solar system scales, eliminating singularities and analyzing thermodynamic quantities on various holographic screens.

Contribution

It introduces a noncommutative spherically symmetric spacetime model and examines its impact on Verlinde's entropic gravity scenario at solar system scales.

Findings

Singularity at the origin is eliminated in the noncommutative spacetime.

Derived thermodynamic quantities like temperature and energy on different holographic screens.

Analyzed modifications to entropic force law due to noncommutative geometry.

Abstract

We first study some aspects of a physically inspired kind of a noncommutative spherically symmetric spacetime based on the Gaussian-smeared mass distribution for a solar system scale. This leads to the elimination of a singularity appeared in the origin of the spacetime. Afterwards, we investigate some features of Verlinde's scenario in the presence of the mentioned spacetime and derive several quantities such as Unruh-Verlinde temperature, the energy and the entropic force on three different types of holographic screens, namely the static, the stretched horizon and the accelerating surface.