The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force

TL;DR

This paper explores how a generalized uncertainty principle with minimal length, minimal momentum, and maximal momentum modifies entropic force, black hole thermodynamics, and Einstein's and Friedmann's equations.

Contribution

It introduces a new GUP framework affecting entropic force, black hole thermodynamics, and gravitational field equations, extending Verlinde's theory with quantum corrections.

Findings

GUP-corrected entropic force depends on black hole properties and Planck scale constants

Derived modified Einstein's field equations incorporating GUP effects

Obtained altered Friedmann equations reflecting quantum gravitational corrections

Abstract

In this paper, the modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole is investigated. Then, according to Verlinde's theory, the generalized uncertainty principle (GUP) corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes, but also to the Planck length and the dimensionless constants $\alpha _{\rm{0}}$ and $\beta _{\rm{0}}$. Moreover, based on the GUP corrected entropic force, we also derive the modified Einstein's field equation (EFE) and the modified Friedmann equation.