Gluing construction of initial data with Kerr-de Sitter ends

TL;DR

This paper develops a gluing method to construct initial data in General Relativity with Kerr-de Sitter ends, extending previous results to non-time-symmetric cases using a deformation approach inspired by Corvino.

Contribution

It introduces a new gluing technique to produce initial data with Kerr-de Sitter ends, expanding on prior work limited to time-symmetric cases.

Findings

Constructed initial data with Kerr-de Sitter ends

Extended previous time-symmetric results

Demonstrated deformation method for non-time-symmetric data

Abstract

We construct initial data sets which satisfy the vacuum constraint equa- tions of General Relativity with positive cosmologigal constant. More pre- silely, we deform initial data with ends asymptotic to Schwarzschild-de Sitter to obtain non-trivial initial data with exactly Kerr-de Sitter ends. The method is inspired from Corvino's gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chru\'sciel and Pollack.