General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry

TL;DR

This paper develops a Hamiltonian formulation of general relativity on null surfaces within teleparallel geometry, avoiding gauge conditions and resulting in a distinct, fully constrained system based on tetrads and torsion.

Contribution

It introduces a novel Hamiltonian framework for general relativity on null surfaces using teleparallel geometry without gauge fixing, differing from ADM formulations.

Findings

Hamiltonian system is fully constrained

Formulation does not impose gauge conditions

Uses tetrads and torsion as fundamental variables

Abstract

The Hamiltonian formulation of general relativity on a null surface is established in the teleparallel geometry. No particular gauge conditons on the tetrads are imposed, such as the time gauge condition. By means of a 3+1 decomposition the resulting Hamiltonian arises as a completely constrained system. However, it is structurally different from the the standard Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the basic field quantities are tetrads that transform under the global SO(3,1) and the torsion tensor.