Self-dual teleparallel gravity and the positive energy theorem

TL;DR

This paper develops a self-dual formulation of teleparallel gravity, deriving a Hamiltonian framework, boundary terms, and extending the positive energy theorem proof to include momentum.

Contribution

It introduces a self-dual Lagrangian for teleparallel gravity, connects it to Ashtekar variables, and extends the positive energy theorem proof to cases with momentum.

Findings

Derived a self-dual Lagrangian equivalent to Ashtekar's in vacuum.

Developed Hamiltonian and constraint analysis for the self-dual formulation.

Extended the positive energy theorem proof to include momentum cases.

Abstract

A self-dual and anti-self-dual decomposition of the teleparallel gravity is carried out and the self-dual Lagrangian of the teleparallel gravity which is equivalent to the Ashtekar Lagrangian in vacuum is obtained. Its Hamiltonian formulation and the constraint analysis are developed. Starting from Witten's equation Nester's gauge condition is derived directly and a new expression of the boundary term is obtained. Using this expression and Witten's identity the proof of the positive energy theorem by Nester et al is extended to a case including momentum.