Conserved quantities on asymptotically hyperbolic initial data sets

Po-Ning Chen Columbia University Mu-Tao Wang Columbia University Shing-Tung Yau Harvard University

Mathematical Physics mathscidoc:1608.10015

2014.9
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and center of mass. Our assumption on the asymptotics is less stringent than any previous ones to validate a Bondi-type mass loss formula. The Lorentz group acts on the asymptotic infinity through the exchange of foliations by coordinate spheres. For foliations aligning with the total energy-momentum vector, we prove that the limits of quasi-local center of mass and angular momentum are finite, and evaluate the limits in terms of the expansion coefficients of the metric and the second fundamental form.
quasi-local conserved quantities, asymptotically hyperbolic
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@inproceedings{po-ning2014conserved,
  title={Conserved quantities on asymptotically hyperbolic initial data sets},
  author={Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820142827526963319},
  year={2014},
}
Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau. Conserved quantities on asymptotically hyperbolic initial data sets. 2014. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820142827526963319.
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