Weyl–Lewis–Papapetrou coordinates

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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]

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 ${\displaystyle (t,\rho ,\phi ,z)}$ are the cylindrical Weyl–Lewis–Papapetrou coordinates in ${\displaystyle 3+1}$-dimensional spacetime, and ${\displaystyle \lambda }$, ${\displaystyle \nu }$, ${\displaystyle \omega }$, and ${\displaystyle B}$, are unknown functions of the spatial non-angular coordinates ${\displaystyle \rho }$ and ${\displaystyle z}$ only. Different authors define the functions of the coordinates differently.

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

• Marek, J.; Sloane, A. (May 1979). "A finite rotating body in general relativity". Il Nuovo Cimento B Series 11. 51 (1): 45–52. Bibcode:1979NCimB..51...45M. doi:10.1007/BF02743695. ISSN 1826-9877. S2CID 125042609.
• Richterek, L.; Novotný, J.; Horský, J. (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.
• Sharif, M. (December 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. ISSN 0103-9733. S2CID 15915449.
• Sloane, A (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. ISSN 0004-9506.

• Friedman, John L.; Stergioulas, Nikolaos (2013). Rotating relativistic stars. Cambridge monographs on mathematical physics. Cambridge University Press. p. 151. ISBN 978-0-521-87254-6.
• Macías, A.; Cervantes-Cota, J. L.; Lämmerzahl, C. (2001). Macías, A.; Cervantes Cota, Jorge Luis; Lämmerzahl, C. (eds.). Exact solutions and scalar fields in gravity: recent developments. New York: Kluwer Academic/Plenum Publishers. p. 39. ISBN 978-0-306-46618-2.
• Das, Anadijiban; DeBenedictis, Andrew (2012). The general theory of relativity: a mathematical exposition. New York London: Springer Publishing. p. 317. ISBN 978-1-4614-3658-4.
• Hall, G. S.; Pulham, J. R. (1996). Hall, G. S.; Pulham, J. R. (eds.). General relativity: proceedings of the forty sixth Scottish Universities summer school in physics, Aberdeen, July 1995. SUSSP publications. Vol. 46. Scottish Universities Summer Schools in Physics ; Institute of Physics Publishing. pp. 65, 73, 78. ISBN 978-0-7503-0395-8.

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