Negative kinetic energy term of general relativity and its removing

TL;DR

This paper introduces a new Lagrangian formulation of general relativity that isolates and removes the negative kinetic energy component, resulting in modified field equations with a different constraint-dynamical structure.

Contribution

It presents a novel Lagrangian for general relativity using vierbein formalism that eliminates negative kinetic energy terms, leading to a new set of field equations.

Findings

Successfully decomposes the kinetic energy term into positive and negative parts.

Proposes gauge conditions to remove the negative kinetic energy term.

Derives a new field equation with altered constraint and dynamical equations count.

Abstract

We first present a new Lagrangian of general relativity, which can be divided into kinetic energy term and potential energy term. Taking advantage of vierbein formalism, we reduce the kinetic energy term to a sum of five positive terms and one negative term. Some gauge conditions removing the negative kinetic energy term are discussed. Finally, we present a Lagrangian that only include positive kinetic energy terms. To remove the negative kinetic energy term leads to a new field equation of general relativity in which there are at least five equations of constraint and at most five dynamical equations, this characteristic is different from the normal Einstein field equation in which there are four equations of constraint and six dynamical equations.