A new geometric invariant on initial data for Einstein equations

TL;DR

This paper introduces a new geometric invariant for asymptotically flat initial data in Einstein's equations that quantifies deviation from stationarity and radiation content.

Contribution

It constructs a novel invariant that measures how far initial data is from stationary solutions, providing a new tool for analyzing Einstein's equations.

Findings

Invariant vanishes for stationary data

Measures total radiation in vacuum cases

Quantifies deviation from stationarity

Abstract

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.