Characteristic Gluing with $\Lambda$ 1. Linearised Einstein equations on four-dimensional spacetimes

TL;DR

This paper proves a new gluing theorem for linearised gravitational fields on characteristic surfaces in four-dimensional spacetimes with a cosmological constant, extending previous Minkowski space results.

Contribution

It introduces a linearised Einstein equations gluing theorem on characteristic surfaces in static vacuum backgrounds with arbitrary topology.

Findings

Establishes a gluing theorem for linearised vacuum gravitational fields with cosmological constant.

Generalises previous Minkowski space results to more general backgrounds.

Provides a mathematical framework for understanding gravitational field modifications on characteristic surfaces.

Abstract

We establish a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic surfaces in static vacuum four-dimensional backgrounds with cosmological constant $\Lambda \in \mathbb{R}$ and arbitrary topology of the compact cross-sections of the null hypersurface. This generalises and complements, in the linearised case, the pioneering analysis of Aretakis, Czimek and Rodnianski, carried-out on light-cones in Minkowski spacetime.