A Local Existence Theorem for the Einstein-Dirac Equation
نویسنده
چکیده
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 admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics η on M × R such that (M × 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. MSC(2000): 53C25, 53C27, 83C05
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تاریخ انتشار 2002