# The problem of characterising stationary data for the vacuum Einstein equations

## TL;DR

This paper investigates conditions on initial data that ensure the evolution under the vacuum Einstein equations admits a time-like Killing vector, advancing the understanding of stationary solutions in general relativity.

## Contribution

It establishes a necessary condition on initial data for the existence of stationary vacuum solutions with a time-like Killing vector.

## Key findings

- Derived a necessary condition for stationary vacuum data
- Enhanced understanding of initial data constraints for Einstein equations
- Progressed towards characterising stationary solutions

## Abstract

We take a step towards characterising stationary data for the vacuum Einstein equations, by finding a necessary condition on initial data for which the evolution is a solution of the vacuum equations admitting a Killing vector, which is time-like at least in some region of the Cauchy development.