Weyl–Lewis–Papapetrou coordinates

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In general relativity, the Weyl–Lewis–Papapetrou coordinates are a set of coordinates, used in the 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]

Details

The square of the line element is of the form:^[4]

${\displaystyle ds^{2}=-e^{2\nu }dt^{2}+\rho ^{2}B^{2}e^{-2\nu }(d\phi -\omega dt)^{2}+e^{2(\lambda -\nu )}(d\rho ^{2}+dz^{2})}$

where (t, ρ, ϕ, z) are the cylindrical Weyl–Lewis–Papapetrou coordinates in 3 + 1 spacetime, and λ, ν, ω, and B, are unknown functions of the spatial non-angular coordinates ρ and z only. Different authors define the functions of the coordinates differently.

See also

• Introduction to the mathematics of general relativity
• Stress–energy tensor
• Metric tensor (general relativity)
• Relativistic angular momentum
• Weyl metrics

References

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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