×

Measuring multipole moments of Weyl metrics by means of gyroscopes. (English) Zbl 0981.83011

Summary: Using the technique of Rindler and Perlick we calculate the total precession per revolution of a gyroscope circumventing the source of Weyl metrics. We establish thereby a link between the multipole moments of the source and an “observable” quantity. Special attention deserves the case of the \(\gamma\)-metric. As an extension of this result we also present the corresponding expressions for some stationary space-times.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1002/andp.19193641006 · JFM 47.0800.01 · doi:10.1002/andp.19193641006
[2] DOI: 10.1002/andp.19193641006 · JFM 47.0800.01 · doi:10.1002/andp.19193641006
[3] DOI: 10.1002/andp.19193641006 · JFM 47.0800.01 · doi:10.1002/andp.19193641006
[4] Hernández-Pastora J. L., Gen. Relativ. Gravit. 26 pp 877– (1994) · doi:10.1007/BF02107146
[5] Herrera L., Class. Quantum Grav. 17 pp 3617– (2000) · Zbl 0972.83012 · doi:10.1088/0264-9381/17/18/302
[6] Herrera L., Class. Quantum Grav. 17 pp 1549– (2000) · Zbl 0980.83012 · doi:10.1088/0264-9381/17/6/315
[7] DOI: 10.1007/BF00757816 · Zbl 0708.53050 · doi:10.1007/BF00757816
[8] Erez G., Bull. Res. Counc. Isr., Sect. F 8 pp 47– (1959)
[9] Quevedo H., Phys. Rev. 33 pp 334– (1986)
[10] DOI: 10.1063/1.1665348 · Zbl 1107.83313 · doi:10.1063/1.1665348
[11] DOI: 10.1063/1.1665348 · Zbl 1107.83313 · doi:10.1063/1.1665348
[12] DOI: 10.1063/1.1665348 · Zbl 1107.83313 · doi:10.1063/1.1665348
[13] DOI: 10.1063/1.1666501 · Zbl 1107.83304 · doi:10.1063/1.1666501
[14] DOI: 10.1103/RevModPhys.52.299 · doi:10.1103/RevModPhys.52.299
[15] DOI: 10.1063/1.525047 · Zbl 0466.53017 · doi:10.1063/1.525047
[16] DOI: 10.1063/1.525148 · Zbl 0471.58030 · doi:10.1063/1.525148
[17] DOI: 10.1063/1.528551 · Zbl 0696.53057 · doi:10.1063/1.528551
[18] Curzon H. E. J., Proc. London Math. Soc. 23 pp 477– (1924)
[19] Hernández-Pastora J. L., Class. Quantum Grav. 10 pp 2581– (1993) · Zbl 0789.35156 · doi:10.1088/0264-9381/10/12/017
[20] DOI: 10.1063/1.1705005 · Zbl 0139.45703 · doi:10.1063/1.1705005
[21] DOI: 10.1063/1.1705005 · Zbl 0139.45703 · doi:10.1063/1.1705005
[22] DOI: 10.1063/1.1705005 · Zbl 0139.45703 · doi:10.1063/1.1705005
[23] DOI: 10.1063/1.1705005 · Zbl 0139.45703 · doi:10.1063/1.1705005
[24] DOI: 10.1063/1.1705005 · Zbl 0139.45703 · doi:10.1063/1.1705005
[25] DOI: 10.1063/1.1705005 · Zbl 0139.45703 · doi:10.1063/1.1705005
[26] Espósito F., Phys. Lett. B 58 pp 357– (1975) · doi:10.1016/0370-2693(75)90673-5
[27] K. S. Virbhadra, ”Directional naked singularity in General Relativity,” preprint gr-qc/9606004.
[28] Hernández-Pastora J. L., Gen. Relativ. Gravit. 30 pp 999– (1998) · Zbl 0941.83007 · doi:10.1023/A:1026644504125
[29] Stephany G., Astron. Astrophys. 350 pp 310– (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.