Asymptotically flat and regular Cauchy data

TL;DR

This paper constructs a broad class of asymptotically flat initial data sets with non-zero mass and angular momentum, featuring detailed asymptotic expansions of the metric and extrinsic curvature at spatial infinity.

Contribution

It introduces a novel method for constructing initial data with specific asymptotic properties, expanding the set of known solutions in general relativity.

Findings

Existence of a large class of initial data with prescribed asymptotic behavior.

Explicit asymptotic expansions of metric and extrinsic curvature.

Relevance for understanding gravitational fields at spatial infinity.

Abstract

I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.