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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]

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

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

Weyl, H. (1917). "Zur Gravitationstheorie". Ann. 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". Roy. Soc., Proc. 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". Proc. R. Irish Acad. A. 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). pp. 45–52. Bibcode:1979NCimB..51...45M. doi:10.1007/BF02743695.
L. Richterek; J. Novotny; J. Horsky (2002). "Einstein−Maxwell fields generated from the gamma-metric and their limits". Czechoslov. J. Phys. 52. p. 2. arXiv:gr-qc/0209094v1. Bibcode:2002CzJPh..52.1021R. 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. 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. 46. Scottish Universities Summer School in Physics. pp. 65, 73, 78. ISBN 075-030-395-6.

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