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

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.