An alternate derivation of Padmanabhan's differential bulk-surface relation in General Relativity

TL;DR

This paper presents an alternative derivation of Padmanabhan's differential bulk-surface relation in General Relativity using gauge theory formulation, linking gravitational information and degrees of freedom.

Contribution

It provides a new derivation based on Gockeler and Schucker's gauge theory approach, connecting entropy functional with the gravitational Lagrangian.

Findings

Rewrites Padmanabhan's entropy functional as a gauge theory Lagrangian

Establishes a link between bulk-surface relation and gauge theory formulation

Offers an alternative perspective on gravitational degrees of freedom

Abstract

A differential bulk-surface relation of the lagrangian of General Relativity has been derived by Padmanabhan. This has relevance to gravitational information and degrees of freedom. An alternate derivation is given based on the differential form gauge theory formulation of gravity due to Gockeler and Schucker. Also an entropy functional of Padmanabhan and Paranjape can be rewritten as the Gockeler and Schucker lagrangian.