Energy, momentum, and center of mass in general relativity

Mu-Tao Wang Columbia University

Differential Geometry mathscidoc:1608.10025

2016.5
These notions in the title are of fundamental importance in any branch of physics. However, there have been great difficulties in finding physically acceptable definitions of them in general relativity since Einstein's time. I shall explain these difficulties and progresses that have been made. In particular, I shall introduce new definitions of center of mass and angular momentum at both the quasi-local and total levels, which are derived from first principles in general relativity and by the method of geometric analysis. With these new definitions, the classical formula p=mv is shown to be consistent with Einstein's field equation for the first time. This paper is based on joint work [14][15] with Po-Ning Chen and Shing-Tung Yau.
general relativity, Einstein's field equation
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@inproceedings{mu-tao2016energy,,
  title={Energy, momentum, and center of mass in general relativity},
  author={Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820161005031173329},
  year={2016},
}
Mu-Tao Wang. Energy, momentum, and center of mass in general relativity. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160820161005031173329.
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