Estimating total momentum at finite distances

TL;DR

This paper investigates the challenges in accurately estimating the total Bondi momentum at finite distances in asymptotically flat spacetimes, emphasizing the importance of accounting for finite distance and gauge effects, especially in numerical simulations.

Contribution

It provides a detailed analysis of the issues involved in computing total momentum at finite distances and offers insights applicable to numerical relativity.

Findings

Finite distance and gauge effects significantly impact momentum calculations.

The discussion aids in improving physical quantity extraction from numerical spacetimes.

Highlights the importance of correct finite distance evaluations for accurate physical insights.

Abstract

We study the difficulties associated with the evaluation of the total Bondi momentum at finite distances around the central source of a general (asymptotically flat) spacetime. Since the total momentum is only rigorously defined at future null infinity, both finite distance and gauge effects must be taken into account for a correct computation of this quantity. Our discussion is applicable in general contexts but is particularly relevant in numerically constructed spacetimes for both extracting important physical information and assessing the accuracy of additional quantities.