Evaluation of the ADM mass and center of mass via the Ricci tensor. (English) Zbl 1335.83012
Summary: 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.
MSC:
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 53Z05 | Applications of differential geometry to physics |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 53C20 | Global Riemannian geometry, including pinching |
Keywords:
ADM mass; center of mass; density theorem; asymptotically flat manifold; Ricci tensor; Hamiltonian formulationReferences:
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