Uniqueness of the mass in the radiating regime

TL;DR

This paper addresses the ambiguity in defining energy for radiating fields, proposing a criterion that ensures a unique, monotonic energy measure for massless scalar and gravitational fields in Minkowski space-time.

Contribution

It introduces a new condition to uniquely define energy in radiating regimes, applicable to scalar and gravitational fields, ensuring monotonicity over retarded time.

Findings

Energy ambiguity resolved for scalar fields using monotonicity

Trautman-Bondi energy shown to be unique and monotonic for gravitational fields

Provides a criterion for unambiguous energy definition in radiating space-times

Abstract

The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski space-time the definition may be rendered unambiguous by adding the requirement that the energy cannot increase in retarded time. We present a similar theorem for the gravitational field, proved elsewhere, which establishes that the Trautman-Bondi energy is the unique (up to a multiplicative factor) functional, within a natural class, which is monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri.