Weyl–Lewis–Papapetrou coordinates
In general relativity, the Weyl–Lewis–Papapetrou coordinates are used in solutions to the vacuum region surrounding an axisymmetric distribution of mass–energy. They are named for Hermann Weyl, Thomas Lewis, and Achilles Papapetrou.[1][2][3]
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Details
The square of the line element is of the form:[4]
where are the cylindrical Weyl–Lewis–Papapetrou coordinates in -dimensional spacetime, and , , , and , are unknown functions of the spatial non-angular coordinates and only. Different authors define the functions of the coordinates differently.
See also
References
- Weyl, H. (1917). "Zur Gravitationstheorie". Annalen der Physik. 54 (18): 117–145. Bibcode:1917AnP...359..117W. doi:10.1002/andp.19173591804.
- Lewis, T. (1932). "Some special solutions of the equations of axially symmetric gravitational fields". Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 136 (829): 176–92. Bibcode:1932RSPSA.136..176L. doi:10.1098/rspa.1932.0073.
- Papapetrou, A. (1948). "A static solution of the equations of the gravitatinal field for an arbitrary charge-distribution". Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences. 52: 191–204. JSTOR 20488481.
- Jiří Bičák; O. Semerák; Jiří Podolský; Martin Žofka (2002). Gravitation, Following the Prague Inspiration: A Volume in Celebration of the 60th Birthday of Jiří Bičák. World Scientific. p. 122. ISBN 981-238-093-0.
Further reading
Selected papers
- J. Marek; A. Sloane (1979). "A finite rotating body in general relativity". Il Nuovo Cimento B. 51 (1): 45–52. Bibcode:1979NCimB..51...45M. doi:10.1007/BF02743695. S2CID 125042609.
- L. Richterek; J. Novotny; J. Horsky (2002). "Einstein–Maxwell fields generated from the gamma-metric and their limits". Czechoslovak Journal of Physics. 52 (9): 1021–1040. arXiv:gr-qc/0209094v1. Bibcode:2002CzJPh..52.1021R. doi:10.1023/A:1020581415399. S2CID 18982611.
- M. Sharif (2007). "Energy-Momentum Distribution of the Weyl–Lewis–Papapetrou and the Levi-Civita Metrics" (PDF). Brazilian Journal of Physics. 37 (4): 1292–1300. arXiv:0711.2721. Bibcode:2007BrJPh..37.1292S. doi:10.1590/S0103-97332007000800017. S2CID 15915449.
- A. Sloane (1978). "The axially symmetric stationary vacuum field equations in Einstein's theory of general relativity". Australian Journal of Physics. 31 (5): 429. Bibcode:1978AuJPh..31..427S. doi:10.1071/PH780427.
Selected books
- J. L. Friedman; N. Stergioulas (2013). Rotating Relativistic Stars. Cambridge Monographs on Mathematical Physics. Cambridge University Press. p. 151. ISBN 978-052-187-254-6.
- A. Macías; J. L. Cervantes-Cota; C. Lämmerzahl (2001). Exact Solutions and Scalar Fields in Gravity: Recent Developments. Springer. p. 39. ISBN 030-646-618-X.
- A. Das; A. DeBenedictis (2012). The General Theory of Relativity: A Mathematical Exposition. Springer. p. 317. ISBN 978-146-143-658-4.
- G. S. Hall; J. R. Pulham (1996). General relativity: proceedings of the forty sixth Scottish Universities summer school in physics, Aberdeen, July 1995. SUSSP proceedings. Vol. 46. Scottish Universities Summer School in Physics. pp. 65, 73, 78. ISBN 075-030-395-6.
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