On Conserved Quantities at Spatial Infinity

TL;DR

This paper investigates the existence of new conserved quantities at spatial infinity within the asymptotic framework of Ashtekar and Romano, revealing hierarchies of conserved quantities for various fields and their persistence in curved space-time.

Contribution

It introduces a characterization of asymptotic behavior of physical fields at spatial infinity and uncovers hierarchies of conserved quantities for different fields, extending known results.

Findings

Hierarchies of conserved quantities are found for Klein-Gordon, Maxwell, and linearized gravitational fields.

Certain conserved quantities from the hierarchy persist in curved space-time.

The asymptotic framework of Ashtekar and Romano is effective for identifying these quantities.

Abstract

There is a well-known short list of asymptotic conserved quantities for a physical system at spatial infinity. We search for new ones.This is carried outwithin the asymptotic framework of Ashtekar and Romano, in which spatial infinity is represented as a smooth boundary of space-time. We first introduce, for physical fields on space-time,a characterization of their asymptotic behavior as certain fields on this boundary. Conserved quantities at spatial infinity, in turn, are constructed from these fields. We find,in Minkowski space-time, that each of a Klein-Gordon field, a Maxwell field, and a linearized gravitational field yields an entire hierarchy of conserved quantities. Only certain quantities in this hierarchy survive into curved space-time.