The Effects of Minimal Length in Entropic Force Approach

Barun Majumder

doi:10.1155/2013/296836

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 aareatype correction term in the entropy-area relation whose consequences in different scenarios are discussed.

Highlights

One of the greatest achievements in theoretical physics is the realization that black holes are well-defined thermodynamic objects with entropy and temperature [1,2,3,4,5]
Gravity may be identified to be associated with entropic force and a thermodynamical system may well describe a gravitational system
This idea came from the thermodynamical interpretation of gravitational field equations

Summary

Introduction

One of the greatest achievements in theoretical physics is the realization that black holes are well-defined thermodynamic objects with entropy and temperature [1,2,3,4,5]. Later modified commutation relations between position and momenta commonly known as the generalized uncertainty principle (GUP) were proposed by string theory, doubly special relativity (DSR), and black hole physics with the prediction of a minimum measurable length [31,32,33,34,35,36,37,38,39,40]. With the GUP as proposed in [42, 43] we can arrive at the corrected entropy-area relation for a black hole which can be written as [44,45,46]. In this paper we will study the effect of this corrected entropy-area relation in the theory of modified Newtonian dynamics (MOND). This equation is the entropy corrected equation for the modified Newtonian dynamics

Entropic Corrections due to GUP and the Newton’s Law of Gravitation

Entropic Corrections due to GUP and the Einstein’s Equation

Discussion