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Multipole moments of stationary space-times. (English) Zbl 1107.83304
Summary: Multipole moments are defined for stationary, asymptotically flat, source-free solutions of Einstein’s equation. There arise two sets of multipole moments, the mass moments and the angular momentum moments. These quantities emerge as tensors at a point \(\Lambda\) ‘at spatial infinity’. They may be expressed as certain combinations of the derivatives at \(\Lambda\) of the norm and twist of the timelike Killing vector. In the Newtonian limit, the moments reduce to the usual multipole moments of the Newtonian potential. Some properties of these moments are derived, and, as an example, the multipole moments of the Kerr solution are discussed.

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
35Q80 Applications of PDE in areas other than physics (MSC2000)
Full Text: DOI
[1] DOI: 10.1063/1.1665348 · Zbl 1107.83313
[2] DOI: 10.1063/1.1665427 · Zbl 1107.83312
[3] DOI: 10.1063/1.1665681 · Zbl 0214.49002
[4] DOI: 10.1063/1.1705193 · Zbl 0149.23503
[5] DOI: 10.1063/1.1705193 · Zbl 0149.23503
[6] DOI: 10.1103/PhysRevLett.26.331
[7] DOI: 10.1103/PhysRevLett.26.331
[8] DOI: 10.1103/PhysRevLett.26.331
[9] DOI: 10.1103/PhysRevLett.26.331
[10] DOI: 10.1103/PhysRev.159.1070
[11] DOI: 10.1063/1.1704350 · Zbl 0142.46305
[12] DOI: 10.1063/1.1666094
[13] DOI: 10.1063/1.1704349
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