# Generalized entropic gravity from modified Unruh temperature

## TL;DR

This paper explores how the generalized uncertainty principle influences gravity by deriving modified Einstein and Newton equations using a generalized Unruh temperature within Verlinde's entropic gravity framework.

## Contribution

It introduces a novel derivation of generalized Einstein and Newton equations incorporating the generalized uncertainty principle and modified Unruh temperature.

## Key findings

- Generalized Einstein equations with a cosmological constant are derived.
- Modified Newton's law and Poisson equation are obtained.
- The generalized equations reduce to standard forms in certain limits.

## Abstract

In this study, the effects of the generalized uncertainty principle on the theory of gravity are analyzed. Inspired by Verlinde's entropic gravity approach and using the modified Unruh temperature, the generalized Einstein field equations with cosmological constant are obtained and corresponding conservation law is investigated. The resulting conservation law of energy-momentum tensor dictates that the generalized Einstein field equations are valid in a very limited range of accelerations. Moreover, the modified Newton's law of gravity and the modified Poisson equation are derived. In a certain limit, these modified equations reduce to their standard forms.