Comments on ``The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential'' by R. da Rocha and W.A. Rodrigues, Jr

TL;DR

This paper critiques recent claims about the exact differential nature of the tetrad gravity Lagrangian in 2D spacetime, clarifying its distinction from the metric formulation and addressing related conjectures.

Contribution

It clarifies that the recent result does not prove the Jackiw conjecture nor contradict previous conclusions, emphasizing differences between tetrad and metric formulations.

Findings

The tetrad formulation differs from the metric formulation of Einstein-Hilbert action.

The recent claim about the Lagrangian being an exact differential does not prove the Jackiw conjecture.

The paper clarifies misconceptions about the implications of the recent result.

Abstract

We argue that the recent result of da Rocha and Rodrigues that in two dimensional spacetime the Lagrangian of tetrad gravity is an exact differential [1], despite the claim of the authors, neither proves the Jackiw conjecture [2], nor contradicts to the conclusion of [3]. This demonstrates that the tetrad formulation is different from the metric formulation of the Einstein-Hilbert action.