On Integrating the Left-Flat Vacuum Einstein Equations
Ezra T. Newman
TL;DR
This paper analyzes the spin-coefficient form of the left-flat vacuum Einstein equations, showing most can be explicitly integrated using potentials, with the remaining equation being a nonlinear wave equation that determines the entire solution.
Contribution
It introduces a method to explicitly integrate most of the left-flat vacuum Einstein equations using spin-weighted potentials, reducing the problem to solving a nonlinear wave equation.
Findings
Most equations are explicitly integrable via potentials.
The remaining nonlinear wave equation determines the entire solution.
Solutions for several special cases are obtained.
Abstract
Considering the spin-coefficient version of the left-flat vacuum Einstein equations, all but one of the fifty equations can be explicitly integrated via the introduction of five spin-weight s=-2 complex potentials. The final equation is a non-linear wave equation for the last of the potentials. Solutions to this equation determine solutions for the entire system. Solutions for several special cases are obtained
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.