Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors

Abstract

Lorentzian manifolds with parallel spinors are important objects of study in several branches of geometry, analysis and mathematical physics. Their Cauchy problem has recently been discussed by Baum, Leistner and Lischewski, who proved that the problem locally has a unique solution up to diffeomorphisms, provided that the intial data given on a space-like hypersurface satisfy some constraint equations. In this article we provide a method to solve these constraint equations. In particular, any curve (resp. closed curve) in the moduli space of Riemannian metrics on $M$ with a parallel spinor gives rise to a solution of the constraint equations on $M\times (a,b)$ (resp. $M\times S^1$).

arXiv commentLast preprint version. The article is open access, see short link https://rdcu.be/crPr1

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