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Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces

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Abstract

We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the assumption of the maximal condition and use a notion of size which is easily computable. Moreover, these results give rise to black hole existence criteria which are meaningful even in the time-symmetric case, and also include certain boundary effects.

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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Marcus Khuri

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Naqing Xie

Authors
  1. Marcus Khuri
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  2. Naqing Xie
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Corresponding author

Correspondence to Naqing Xie.

Additional information

Communicated by James A. Isenberg.

Dedicated to the memory of our late friend and colleague Sergio Dain.

M. Khuri acknowledges the support of NSF Grant DMS-1308753. N. Xie is partially supported by the National Science Foundation of China Grants Nos. 11671089, 11421061.

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Khuri, M., Xie, N. Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces. Ann. Henri Poincaré 18, 2815–2830 (2017). https://doi.org/10.1007/s00023-017-0582-1

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  • DOI: https://doi.org/10.1007/s00023-017-0582-1

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