ADM, BMS, and some puzzling interconnections

TL;DR

This paper explores the complex relationship between ADM and BMS formalisms in gravitational physics, addressing puzzles like local energy conservation and clarifying recent developments in angular momentum and radiation in asymptotically flat spacetimes.

Contribution

It offers new insights into the connection between ADM and BMS quantities, resolving puzzles related to energy and angular momentum in gravitational scattering.

Findings

Clarified the physical meaning of local-in-angle energy conservation.

Connected ADM and BMS quantities in stationary spacetimes.

Resolved recent debates on angular momentum loss and radiation.

Abstract

The precise connection between the ADM and BMS formalisms is still far from being fully understood. It leads superficially to some puzzles whose resolution can provide new interesting physical insights. One example concerns the claimed local-in-angle conservation of energy in a gravitational scattering process, whose physical meaning I will try to clarify in an explicit example. As my main topic, I will sketch my own understanding of how a recent saga on the definition of angular momentum, its loss, and its radiation, appears to have found its way to a happy ending by appealing to some non-trivial connections between ADM and BMS quantities in asymptotically flat and stationary spacetimes.