Hamiltonian description of radiation phenomena: Trautman-Bondi energy and corner conditions

TL;DR

This paper develops a Hamiltonian framework for radiation phenomena using Trautman-Bondi energy, incorporating radiation data at null infinity to accurately describe corner conditions in the initial value problem.

Contribution

It introduces a Hamiltonian formulation that includes radiation data at null infinity, providing a new perspective on corner conditions in radiation phenomena.

Findings

Cauchy problem on a hyperboloid defines a Hamiltonian system with radiation data.

Trautman-Bondi mass and radiated energy serve as the Hamiltonian.

Correctly describes corner conditions in the presence of radiation.

Abstract

Cauchy initial value problem on a hyperboloid is proved to define a Hamiltonian system, provided the radiation data at null infinity are also taken into account, as a part of Cauchy data. The "Trautman-Bondi mass", supplemented by the "already radiated energy" assigned to radiation data, plays role of the Hamiltonian function. This approach leads to correct description of the corner conditions.