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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    Lan-Hsuan Huang & Mu-Tao Wang

  2. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Richard Schoen

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  1. Lan-Hsuan Huang
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  2. Richard Schoen
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  3. Mu-Tao Wang
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Correspondence to Richard Schoen.

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Communicated by P.T. Chruściel

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Huang, LH., Schoen, R. & Wang, MT. Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets. Commun. Math. Phys. 306, 785–803 (2011). https://doi.org/10.1007/s00220-011-1295-9

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  • DOI: https://doi.org/10.1007/s00220-011-1295-9

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