How can rainbow gravity affect on gravitational force?

TL;DR

This paper explores how rainbow gravity modifies black hole entropy and investigates its effects on gravitational laws and dynamics through an entropic force framework.

Contribution

It derives entropy corrections in rainbow gravity and studies their impact on Newtonian and Einsteinian gravity using Verlinde's entropic force approach.

Findings

Rainbow gravity introduces entropy-area law corrections.

Modified entropy affects Newton's law and Einstein's equations.

Implications for gravitational dynamics in rainbow gravity.

Abstract

According to Verlinde's recent proposal, the gravity is originally an entropic force. In this work, we obtain the corrections to the entropy-area law of black holes within rainbow gravity. The corrected entropy-area law leads to the modifications of the number of bits $N$. Inspired by Verlinde's argument on the entropic force, and using the modified number of bits, we can investigate the effects of rainbow gravity on the modified Newtonian dynamics, Newton's law of gravitation, and Einstein's general relativity in entropic force approach.