The Effects of Minimal Length in Entropic Force Approach

Abstract

With Verlinde's recent proposal which says that gravity can be identified with an entropic force and considering the effects of generalized uncertainty principle in the black hole entropy-area relation we derive the modified equations for Newton's law of gravitation, modified Newtonian dynamics and Einstein's general relativity. The corrections to the Newtonian potential is compared with the corrections that come from Randall-Sundrum II model and an effective field theoretical model of quantum general relativity. The effect of the generalized uncertainty principle introduces a $\sqrt{\text{Area}}$ type correction term in the entropy area relation whose consequences in different scenarios are discussed.

12 pages, to appear in Advances in High Energy Physics

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• Rainbow gravity corrections to the entropic force
• Entropic corrected Newton's law of gravitation and the Loop Quantum Black Hole gravitational atom
• Probing Short Gravity using Temporal Lensing
• Quantum tunneling driven by quintessence and the role of GUP