General Relativity as a fully singular Lagrange system

TL;DR

This paper reformulates general relativity as a fully singular Lagrange system by introducing gauge conditions that eliminate second time derivatives in the Einstein equations, simplifying the Lagrangian structure.

Contribution

It introduces gauge conditions and a corresponding Lagrangian that remove second time derivatives, making general relativity a fully singular Lagrange system.

Findings

Elimination of second time derivatives in Einstein equations

A new Lagrangian formulation without quadratic first derivatives

Simplification of the mathematical structure of general relativity

Abstract

We present some gauge conditions to eliminate all second time derivative terms in the vierbein forms of the ten Einstein equations of general relativity; at the same time, we present the corresponding Lagrangian in which there is not any quadratic term of first time derivative that can leads to those vierbein forms of the Einstein equations without second time derivative term by the corresponding Euler-Lagrange equations. General relativity thus becomes a fully singular Lagrange system.