Perturbative Solutions of the Extended Constraint Equations in General Relativity

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dc.creatorButscher, Adrian
dc.date2002-11-11
dc.date2006-09-08
dc.date.accessioned2026-07-07T10:31:56Z
dc.date.available2026-07-07T10:31:56Z
dc.descriptionThe extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.
dc.descriptionThis third and final version has been accepted for publication in Communications in Mathematical Physics
dc.identifierhttps://arxiv.org/abs/gr-qc/0211037
dc.identifierhttp://arxiv.org/abs/gr-qc/0211037
dc.identifierCommun.Math.Phys.272:1-23,2007
dc.identifierdoi:10.1007/s00220-007-0204-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/178588
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectDifferential Geometry
dc.titlePerturbative Solutions of the Extended Constraint Equations in General Relativity
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