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

2014/08/18 by Pengzi Miao, Miao, Pengzi, Luen-Fai Tam +1 · 3 citations
Physics and Astronomy · Mathematics · #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.1408.3893

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 Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the same.

Citations

• The mass of an asymptotically flat manifold
• The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation

Cited by

• Foliations by critical surfaces of the Hawking energy in asymptotically flat initial data sets
• Geometric inequalities for electrostatic systems with boundary
• Chern's magic form and the Gauss-Bonnet-Chern mass

Related

• Evaluation of the mass of an asymptotically hyperbolic manifold
• A generalization of the ADM mass for asymptotically Euclidean manifolds of weak regularity
• Chern's magic form and the Gauss-Bonnet-Chern mass
• Mass under the Ricci flow
• Some lower estimates of ADM mass and Brown-York mass