Some aspects of entropic gravity in the presence of a noncommutative Schwarzschild-deSitter black hole

TL;DR

This paper explores how noncommutative geometry affects entropic gravity near Schwarzschild-deSitter black holes, revealing finite cut-offs and potential violations of the equivalence principle due to quantum effects.

Contribution

It introduces a model combining noncommutative geometry with entropic gravity in Schwarzschild-deSitter spacetime, highlighting finite scale cut-offs and modifications to gravitational behavior.

Findings

Existence of finite cut-offs at short and long distances where force and energy abruptly stop.

Presence of a noncommutative-induced deSitter core near the origin.

Derivation of an effective gravitational constant indicating quantum fluctuations.

Abstract

We study some features of entropic force approach in the presence of a noncommutative Schwarzschild-deSitter black hole. In this setup, there exists a similarity between the small and large scales. There are two finite cut-off in very short and long distances wherein the force and energy graph stop abruptly at those scales. We find that the existence of a deSitter core around the origin, induced by noncommutativity, in addition to a standard deSitter background at large scale may lead to a violation of the equivalence principle. Finally in order to directly observe the finite cut-off at short-scale gravity, caused by noncommutativity quantum fluctuations, we derive an effective gravitational constant.