Rainbow gravity corrections to the entropic force

TL;DR

This paper investigates quantum gravity corrections to the entropic force within a rainbow gravity framework, deriving modified thermodynamics, Einstein's equations, and Friedmann equations influenced by rainbow parameters and Planck length.

Contribution

It introduces a novel approach to incorporate rainbow gravity effects into entropic force theory, deriving new corrected equations and thermodynamics for black holes.

Findings

Modified entropic force depends on black hole properties, Planck length, and rainbow parameter.

Derived corrected Einstein's field equations incorporating rainbow gravity effects.

Obtained modified Friedmann equations consistent with rainbow gravity corrections.

Abstract

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein's field equation, Newton's law of gravitation and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde's theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also the Planck length $\ell_p$, and the rainbow parameter $\gamma$. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein's field equation and the modified Friedmann equation are also derived.