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

TL;DR

This paper demonstrates how to perturb vacuum asymptotically flat spacetimes to achieve specified center of mass and angular momentum values while maintaining the same energy and linear momentum, using explicit linear perturbations near infinity.

Contribution

It introduces a method to precisely control center of mass and angular momentum in vacuum initial data sets through explicit perturbations near infinity.

Findings

Can prescribe center of mass and angular momentum independently

Perturbation preserves energy and linear momentum

Explicit construction of perturbations provided

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.