Supertranslations at Spatial and Timelike Infinities in the First-Order Formalism

TL;DR

This paper investigates supertranslations at spatial and timelike infinities using the first-order formalism, relaxing boundary conditions, and deriving Hamiltonian charges that align with metric-based results.

Contribution

It introduces a first-order formalism approach to supertranslations at infinities, relaxing boundary conditions and deriving consistent Hamiltonian charges.

Findings

Hamiltonian charges for supertranslations are derived.

Charges match metric-based expressions.

Boundary conditions are relaxed to include supertranslations.

Abstract

We study supertranslations at spatial and future timelike infinity in the first-order formalism. We relax the Ashtekar-Engle-Sloan boundary conditions to allow supertranslations at the spatial infinity and obtain the precise form of the tetrads and Lorentz connections. Employing the covariant phase space technique we obtain the Hamiltonian charges for the supertranslations at both timelike and spatial infinities. The charges obtained are shown to match the expressions reported adopting the metric-based approach.