Abstract:We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using the Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using the Ricci tensor are the same.
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- Pengzi Miao
- Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
- MR Author ID: 715810
- Email: email@example.com
- Luen-Fai Tam
- Affiliation: The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China
- MR Author ID: 170445
- Email: firstname.lastname@example.org
- Received by editor(s): August 26, 2014
- Received by editor(s) in revised form: January 16, 2015
- Published electronically: October 6, 2015
- Additional Notes: The first author’s research was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105.
The second author’s research was partially supported by Hong Kong RGC General Research Fund #CUHK 403108
- Communicated by: Lei Ni
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 753-761
- MSC (2010): Primary 83C99; Secondary 53C20
- DOI: https://doi.org/10.1090/proc12726
- MathSciNet review: 3430851