Modified entropies, their corresponding Newtonian forces, potentials, and temperatures

TL;DR

This paper explores how replacing Boltzmann entropy with generalized, non-extensive entropies affects Newtonian forces, potentials, and black hole temperature corrections within the entropic gravity framework.

Contribution

It introduces a method to derive generalized Newtonian forces and potentials using non-extensive entropies, extending the entropic gravity hypothesis.

Findings

Derived modified Newtonian forces and potentials from non-extensive entropies.

Calculated corrections to black hole temperature based on generalized entropies.

Discussed the implications of correction terms on gravitational and thermodynamic properties.

Abstract

Assuming the hypothesis of the entropic nature of gravity, we calculate generalized Newtonian forces, their associated potentials and field equations, when other, in general non-extensive, entropies are considered instead of the usual Boltzmann entropy. Some comments about the nature of the correction terms presented are given, and a calculation of corrections to the Bekenstein-Hawking temperature is performed using the arguments which lead to what can be called a Michell-Laplace black hole.