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 type correction term in the entropy-area relation whose consequences in different scenarios are discussed. 1. Introduction One of the greatest achievements in theoretical physics is the realization that black holes are well-defined thermodynamic objects with entropy and temperature [1–5]. Hawking [4, 5] has derived that a Schwarzschild black hole emits a thermal radiation whose temperature depends on the mass of the black hole and is given by . Also Bekenstein has shown that a black hole has a well-defined entropy and is proportional to the area of the black hole horizon given by the entropy-area relation Here is the cross-sectional area of the black hole horizon and is the Planck length. Recently there has been much interest devoted to the leading order quantum corrections of the black hole entropy-area relation. Entropy accounts for the number of microstates of the system as it has a definite statistical meaning in thermodynamics. Sakharov is the originator of the idea of emergent gravity [6]. Jacobson [7] was the first to view Einstein’s equation as an equation of state. Together with the second law of thermodynamics and the fact that entropy is proportional to the horizon area he derived the Einstein’s equations. Later several studies were carried out to understand the deeper underlying connection between horizon thermodynamics and Einstein’s equation. Padmanabhan showed that for a wider class of theories the gravitational field equations on the horizon can be reduced to the first law of thermodynamics arguing the Einstein’s equation to be a thermodynamic entity [8]. This novel idea was also later introduced in modified theories of gravity [9]. For a brief review on the demonstration of the idea in other scenarios we refer to [10–16]. The development in the lines discussed here refers to the point that thermodynamic properties can be associated with the horizon and gravity can be thought of as an entity whose origin is statistical in nature. Recently Verlinde [17] introduced
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