Modified Newton's gravitational law from deformed Poisson bracket

Abstract

In this paper, we obtain the modified Newton's gravitational law from deformed Poisson bracket motivated by the generalized uncertainty principle. The modified Newton's gravitational law that we obtain contains a term that plays an important role only in the regime of first order in $\bar{\beta}$. In the ordinary situation or condition, the modified Newton's gravitational law reduces to the conventional Newton's gravitational law.