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, T. Lewis, and Achilles Papapetrou.^[1][2][3]

Details

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

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 Series 11. 51 (1). pp. 45–52. 
• L. Richterek; J. Novotny; J. Horsky (2002). "Einstein−Maxwell fields generated from the gamma-metric and their limits" (PDF). Czech.J.Phys. 52. p. 2. arXiv:gr-qc/0209094v1 . doi:10.1023/A:1020581415399. 
• M. Sharif (2007). "Energy-Momentum Distribution of the Weyl−Lewis−Papapetrou and the Levi-Civita Metrics" (PDF). Brazilian Journal of Physics. 37. 
• A. Sloane (1978). "The axially symmetric stationary vacuum field equations in Einstein's theory of general relativity". Aust. J. Phys. 31. CSIRO. p. 429. Bibcode:1978AuJPh..31..427S. 

Selected books

• J. L. Friedman; N. Stergioulas (2013). Rotating Relativistic Stars. Cambridge Monographs on Mathematical Physics. Cambridge University Press. p. 151. ISBN 052-187-254-5. 
• 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 146-143-658-3. 
• 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. 46. Scottish Universities Summer School in Physics. pp. 65, 73, 78. ISBN 075-030-395-6.