The signature of the quadratic generalized uncertainty principle on the newtonian gravity and galaxy mass profile

Abstract

In this study, we discuss the corrections implies by the presence of the general uncertainty principle (GUP) on Newton’s law of gravity by virtue of Verlinde’s proposal. We argue here that GUP leads to twofold modification, namely on the equipartition theorem and the holographic relation (Bekenstein-Hawking formula). Hence, following Verlinde’s proposal, we obtain quantum corrections term to the Newtonian gravity. In addition, we also report the quantum corrected mass profile of the galaxy. We restricted our derivation to first order in the GUP’s free parameter and compared it analytically with the other relevant works.