Bondi mass in classical field theory

TL;DR

This paper investigates the Bondi mass and related conserved quantities in classical field theories like electrodynamics and linearized gravity, providing new gauge-invariant formulations and interpretations of mass loss and angular momentum at null infinity.

Contribution

It introduces a gauge-invariant, quasi-local framework for analyzing Bondi mass and angular momentum in linearized gravity and related field theories, connecting linearized and nonlinear asymptotic structures.

Findings

Derived generating formulas on hyperboloids and null surfaces.

Reinterpreted Bondi mass loss in a new gauge-invariant context.

Established relations between linearized and nonlinear asymptotic regimes.

Abstract

We analyze three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. We derive certain generating formula on a hyperboloid and on a null surface for them. The linearized Einstein equations are analyzed around null infinity. It is shown how the dynamics can be reduced to gauge invariant quanitities in a quasi-local way. The quasi-local gauge-invariant ``density'' of the hamiltonian is derived on the hyperboloid and on the future null infinity. The result gives a new interpretation of the Bondi mass loss formula. We show also how to define angular momentum. Starting from affine approach for Einstein equations we obtain variational formulae for Bondi-Sachs type metrics related with energy and angular momentum generators. The original van der Burg asymptotic hierarchy is revisited and the relations between linearized and asymptotic nonlinear situations are established. We discuss also supertranslations, Newman-Penrose charges and Janis solutions.