Consistent Levi Civita truncation uniquely characterizes the Lovelock Lagrangians

TL;DR

This paper introduces the concept of Levi Civita truncation in the Palatini formulation and demonstrates that its consistency uniquely characterizes the Lovelock Lagrangians, providing a new criterion for their identification.

Contribution

The paper defines Levi Civita truncation for Lagrangians in the Palatini formulation and proves it uniquely characterizes Lovelock Lagrangians.

Findings

Levi Civita truncation is well-defined in the Palatini formulation.

Consistency of truncation uniquely identifies Lovelock Lagrangians.

Provides a new characterization criterion for Lovelock theories.

Abstract

We define the concept of Levi Civita truncation for a Lagrangian in the Palatini formulation with an arbitrary connection, and show that its consistency uniquely identifies the Lovelock Lagrangians.