Lagrangian and Hamiltonian for the Bondi-Sachs metrics

TL;DR

This paper derives the Hilbert action for Bondi-Sachs metrics, obtaining Einstein's vacuum equations and exploring the Hamiltonian formulation using Dirac's method for constrained systems.

Contribution

It provides a novel Hamiltonian formulation for Bondi-Sachs metrics based on the Dirac approach, linking the Lagrangian and Hamiltonian frameworks.

Findings

Hilbert action yields Einstein vacuum equations in closed form

Hamiltonian formulation developed using Dirac's constrained system approach

Provides insights into the structure of Bondi-Sachs spacetimes

Abstract

We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation.