Perturbative Solutions of the Extended Constraint Equations in General Relativity |
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Authors: | Adrian Butscher |
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Institution: | (1) Department of Mathematics, University of Toronto, Toronto, ON, M1C 1A4, Canada |
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Abstract: | The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial
data hypersurface in an asymptotically simple space-time 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 , and are equivalent to the usual constraint equations that satisfies as a space-like hypersurface in a space-time 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. |
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Keywords: | |
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