$pp$-wave initial data

TL;DR

This paper constructs initial data for vacuum $pp$-wave spacetimes in four dimensions, ensuring the data evolves into a vacuum $pp$-wave, with conditions based on fundamental forms and conformal Killing initial data.

Contribution

It provides a characterization of vacuum $pp$-wave initial data sets with specific conditions ensuring the evolution remains a vacuum $pp$-wave, combining geometric and conformal Killing data.

Findings

Defines initial data conditions for vacuum $pp$-waves

Links initial data to conformal Killing structures

Ensures data development remains within vacuum $pp$-waves

Abstract

An initial data characterization for vacuum $pp$-wave spacetimes in dimension four is constructed. This is a vacuum initial data set plus some extra conditions guaranteeing that the data development is a subset of a vacuum $pp$-wave. Some of the extra conditions only depend on the same quantities used to construct the vacuum initial data, namely the first and the second fundamental forms while others are related to a conformal Killing initial data characterization (CKID).