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Evaluation of the ADM mass and center of mass via the Ricci tensor


Authors: Pengzi Miao and Luen-Fai Tam
Journal: Proc. Amer. Math. Soc. 144 (2016), 753-761
MSC (2010): Primary 83C99; Secondary 53C20
DOI: https://doi.org/10.1090/proc12726
Published electronically: October 6, 2015
MathSciNet review: 3430851
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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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Additional Information

Pengzi Miao
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
Email: pengzim@math.miami.edu

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
Email: lftam@math.cuhk.edu.hk

DOI: https://doi.org/10.1090/proc12726
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
Article copyright: © Copyright 2015 American Mathematical Society