Initial data for Einstein's equations with superposed gravitational waves

TL;DR

This paper introduces a method to generate initial data for Einstein's equations by superposing gravitational waves on stationary backgrounds, enabling detailed control and large amplitudes, useful for simulations.

Contribution

It combines the conformal thin sandwich formalism with linear gravitational waves to create a covariant, flexible approach for initial data construction with large amplitude waves.

Findings

Allows detailed control over wave shape, location, and direction.

Supports very large amplitude gravitational waves.

Fully covariant with respect to spatial coordinate changes.

Abstract

A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with linear gravitational waves, and allows detailed control over characteristics of the superposed gravitational wave like shape, location and propagation direction. It is furthermore fully covariant with respect to spatial coordinate changes and allows for very large amplitude of the gravitational wave.