Emergent Gravity from an Augmented Variational Principle

TL;DR

This paper establishes a novel connection between Padmanabhan's entropy in emergent gravity and the standard general relativity action using Augmented Variational Principles, clarifying the role of background metrics.

Contribution

It introduces a new approach linking emergent gravity entropy to GR action via AVP, providing insights into the variation process and background metric role.

Findings

Established a direct link between Padmanabhan's entropy and GR action.

Clarified the role of background metrics in emergent gravity.

Demonstrated the use of AVP in deriving gravitational dynamics.

Abstract

A direct and non-trivial link between Padmanabhan's entropy used in emergent gravity and standard GR action is established. To do that, Augmented Variational Principles (AVP) will be used. We shall discuss how this link accounts for the details of the variation of Padmanabhan's action based on gravitational entropy. It will also clarify the role of the background metric and its non-dynamical role.