On the validity of the definition of angular momentum in general relativity
Po-Ning Chen, Lan-Hsuan Huang, Mu-Tao Wang, Shing-Tung Yau
TL;DR
This paper investigates the validity of the ADM angular momentum definition in general relativity without parity assumptions, providing explicit examples and discussing related concepts like center of mass in different spacetimes.
Contribution
It presents explicit examples of asymptotically flat hypersurfaces with zero energy-momentum but non-zero angular momentum, challenging previous assumptions.
Findings
Explicit examples in Minkowski spacetime with zero ADM energy but finite angular momentum.
Discussion of the Beig-Ó Murchadha-Regge-Teitelboim center of mass.
Analysis of analogous examples in Schwarzschild spacetime.
Abstract
We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-\'O Murchadha-Regge-Teitelboim center of mass and study analogous examples in the Schwarzschild spacetime.
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Taxonomy
TopicsRelativity and Gravitational Theory · Black Holes and Theoretical Physics · Advanced Differential Geometry Research