Specifying angular momentum and center of mass for vacuum initial data sets

Abstract

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.

(v2) a minor change in the introduction and a remark added after Theorem 2.1; (v3) final version, appeared in Comm. Math. Phys

References in corpus (5)

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• Construction of N-body initial data sets in general relativity
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• Localized deformation for initial data sets with the dominant energy condition
• Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
• Long time existence from interior gluing
• Recent progress on the positive energy theorem
• The Positive Mass Theorem with Angular Momentum and Charge for Manifolds with Boundary