Gravitational energy-momentum and the Hamiltonian formulation of the teleparallel gravity

TL;DR

This paper analyzes the transformation properties of gravitational energy-momentum in teleparallel gravity, showing its covariance under coordinate transformations but not under local Lorentz transformations, and presents a Hamiltonian formulation with constraints similar to general relativity.

Contribution

It provides a simplified Hamiltonian formulation of teleparallel gravity and clarifies the covariance properties of gravitational energy-momentum.

Findings

Energy-momentum expressed via Lorentz gauge potential is not Lorentz covariant.

Energy-momentum expressed via translation gauge field strength is coordinate covariant.

Constraint algebra matches that of general relativity, indicating their equivalence.

Abstract

The transformation properties of the gravitational energy-momentum in the teleparallel gravity are analyzed. It is proved that the gravitational energy-momentum in the teleparallel gravity can be expressed in terms of the Lorentz gauge potential, and therefore is not covariant under local Lorentz transformations. On the other hand, it can also be expressed in terms of the translation gauge field strength, and therefore is covariant under general coordinate transformations. A simplified Hamiltonian formulation of the teleparallel gravity is given. Its constraint algebra has the same structure as that of general relativity, which indicates the equivalence between the teleparallel gravity and general relativity in the Hamiltonian formulation.