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# Advances in Theoretical and Mathematical Physics

## Volume 20 (2016)

### Number 6

### Conserved quantities on asymptotically hyperbolic initial data sets

Pages: 1337 – 1375

DOI: http://dx.doi.org/10.4310/ATMP.2016.v20.n6.a2

#### Authors

#### Abstract

In this article, we consider the limit of quasi-local conserved quantities 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.