Lovelock gravity from entropic force

TL;DR

This paper extends the entropic gravity framework to higher dimensions, deriving Lovelock gravity and related equations, thereby providing a novel thermodynamic perspective on complex gravitational theories.

Contribution

It introduces a generalized entropic gravity formulation for (n+1)-dimensional spacetime and derives Lovelock gravity equations from entropic principles, linking thermodynamics and higher-dimensional gravity.

Findings

Derived Newton's law and Friedmann equations in Lovelock gravity

Established the higher-dimensional gravitational coupling constant

Confirmed consistency with weak field limit results

Abstract

In this paper, we first generalize the formulation of entropic gravity to (n+1)-dimensional spacetime. Then, we propose an entropic origin for Gauss-Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we are able to derive Newton's law of gravitation as well as the corresponding Friedmann equations in these gravity theories. This procedure naturally leads to a derivation of the higher dimensional gravitational coupling constant of Friedmann/Einstein equation which is in complete agreement with the results obtained by comparing the weak field limit of Einstein equation with Poisson equation in higher dimensions. Our study shows that the approach presented here is powerful enough to derive the gravitational field equations in any gravity theory. PACS: 04.20.Cv, 04.50.-h, 04.70.Dy.