Publication
Perturbative solutions of the extended Einstein constraint equations
Abstract
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface Z in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on Z, and are equivalent to the usual constraint equations that Z satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.
Download publicationRelated Resources
See what’s new.
2016
Printone: Interactive Resonance Simulation for Free-form Print-wind Instrument DesignThis paper presents an interactive design interface for…
2022
A force-mediated controller for cooperative object manipulation with independent autonomous robotsWe consider cooperative manipulation by multiple robots assisting a…
2017
Beyond heuristics: A novel design space model for generative space planning in architectureThis paper proposes a novel design space model which can be used in…
2020
Contrastive Multi-View Representation Learning on GraphsWe introduce a self-supervised approach for learning node and graph…
Get in touch
Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.
Contact us