Conserved quantities on asymptotically hyperbolic initial data sets

2014/09/05 by Po-Ning Chen, Mu-Tao Wang, Chen, Po-Ning +5 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.1409.1812

30 pages

arxiv created 2014/09/05 · openalex publication_date 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and center of mass. Our assumption on the asymptotics is less stringent than any previous ones to validate a Bondi-type mass loss formula. The Lorentz group acts on the asymptotic infinity through the exchange of foliations by coordinate spheres. For foliations aligning with the total energy-momentum vector, we prove that the limits of quasi-local center of mass and angular momentum are finite, and evaluate the limits in terms of the expansion coefficients of the metric and the second fundamental form.

Cited by

• Dynamics of geometric invariants in the asymptotically hyperboloidal setting: energy and linear momentum
• Quasi-local energy with respect to de Sitter/anti-de Sitter reference

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