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Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets

Lan-Hsuan Huang University of Connecticut Richard Schoen Stanford University Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10040

Communications in Mathematical Physics, 306, (3), 785–803, 2011.9
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.
Angular Momentum, vacuum constraint equations
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@inproceedings{lan-hsuan2011specifying,
  title={Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets},
  author={Lan-Hsuan Huang, Richard Schoen, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820184258834682344},
  booktitle={Communications in Mathematical Physics},
  volume={306},
  number={3},
  pages={785–803},
  year={2011},
}
Lan-Hsuan Huang, Richard Schoen, and Mu-Tao Wang. Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets. 2011. Vol. 306. In Communications in Mathematical Physics. pp.785–803. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820184258834682344.
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