Counter-term for the Palatini action of general relativity

TL;DR

This paper analyzes the counter-term in the Palatini formulation of general relativity, demonstrating its equivalence with the Einstein-Hilbert approach for both null and non-null boundaries.

Contribution

It provides a unified expression for the counter-term in the Palatini framework, extending previous results to different boundary types.

Findings

Counter-term expression valid for null and non-null boundaries

Results coincide with previous Einstein-Hilbert based findings

Unifies boundary treatment in Palatini and Einstein-Hilbert formalisms

Abstract

In this paper, we analysis the counter-term for the general relativity in the Palatini framework. The expression is valid for both the null boundary and non-null boundary. We show that final results coincide with that in Ref.\cite{pad1} which starts form the Einstein-Hilbert action.