On the Asymptotics for the Vacuum Einstein Constraint Equations

Abstract

Given asymptotically flat initial data on M^3 for the vacuum Einstein field equation, and given a bounded domain in M, we construct solutions of the vacuum constraint equations which agree with the original data inside the given domain, and are identical to that of a suitable Kerr slice (or identical to a member of some other admissible family of solutions) outside a large ball in a given end. The data for which this construction works is shown to be dense in an appropriate topology on the space of asymptotically flat solutions of the vacuum constraints. This construction generalizes work of the first author, where the time-symmetric case was studied.

28 pages

References in corpus (1)

• On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications

Cited by in corpus (14)

• Stability of Black Holes and Black Branes
• KIDs are non-generic
• Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
• Initial boundary value problems for Einstein's field equations and geometric uniqueness
• Static vacuum solutions from convergent null data expansions at space-like infinity
• Manifold structures for sets of solutions of the general relativistic constraint equations
• Phase space for the Einstein equations
• Numerical calculations near spatial infinity
• Elliptic systems
• Recent results in mathematical relativity
• On black holes as inner boundaries for the constraint equations
• Smoothness at null infinity and the structure of initial data
• Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant
• Foliations of asymptotically flat 3-manifolds by 2-surfaces of prescribed mean curvature