Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 6

Conserved quantities on asymptotically hyperbolic initial data sets

Pages: 1337 – 1375



Po-Ning Chen (Department of Mathematics, University of California at Riverside)

Mu-Tao Wang (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


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.

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Published 2 February 2017