A local existence theorem for the Einstein–Dirac equation

✍ Scribed by Eui Chul Kim

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 225 KB
• Volume: 44
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00133-x

✦ Synopsis

We studied 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 η on M n × R such that (M n × R, η) 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.