2012/07/18 by Norman Gürlebeck, Gürlebeck, Norman
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.48550/arxiv.1207.4500
16 pages, 1 figure
arxiv created 2012/07/18 · openalex publication_date 2012/07/18 · arxiv updated 2012/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we derive source integrals for multipole moments in axially symmetric and static spacetimes. The multipole moments can be read off the asymptotics of the metric close to spatial infinity in a hypersurface, which is orthogonal to the timelike Killing vector. Whereas for the evaluation of the source integrals the geometry needs to be known in a compact region of this hypersurface, which encloses all source, i.e. matter as well as singularities. The source integrals can be written either as volume integrals over such a region or in quasi-local form as integrals over the surface of that region.