8 research outputs found
Perturbative Solutions of the Extended Constraint Equations in General Relativity
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 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 , and are equivalent to the usual constraint equations that 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.Comment: This third and final version has been accepted for publication in
Communications in Mathematical Physic