Weyl–Lewis–Papapetrou coordinates

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${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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In

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.
  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.
  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.
  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.
  doi:10.1071/PH780427
  .

Selected books

• J. L. Friedman; N. Stergioulas (2013). Rotating Relativistic Stars. Cambridge Monographs on Mathematical Physics.
  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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