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.
2008
PieCursor: Merging Pointing and Command Selection for Rapid In-place Tool SwitchingWe describe a new type of graphical user interface widget called the…
1992
The Envoy System: An Open Architecture for AgentsThe Envoy Framework addresses a need for computer-based assistants or…
2013
The Method of Cyclic Intrepid Projections: Convergence Analysis and Numerical ExperimentsThe convex feasibility problem asks to find a point in the…
2016
A Quantum of Continuous Simulated TimeIn the context of discrete-event simulation, time resolution pertains…
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