A Local Existence Theorem for the Einstein-Dirac Equation

Abstract

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold $M^n$ admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics $\bar{\eta }$ on $M^n\times \mathbb{R}$ such that $(M^n\times \mathbb{R},\bar{\eta })$ admit Einstein spinors (resp. weak Killing spinors). To prove the result we split the Einstein-Dirac equation into evolution equations and constraints, by means of Cartan's frame formalism, and apply the local preservation property of constraints.

Latex2e, 34 pages

References in corpus (2)

• The Einstein-Dirac Equation on Riemannian Spin Manifolds
• Solutions of the Einstein-Dirac Equation on Riemannian 3-Manifolds with Constant Scalar Curvature

Cited by in corpus (2)

• The Cauchy problems for Einstein metrics and parallel spinors
• Some extensions of the Einstein-Dirac equation