Weyl−Lewis−Papapetrou coordinates

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

1. Weyl, H. (1917). "Zur Gravitationstheorie". Ann. der Physik. 54: 117–145. doi:10.1002/andp.19173591804.
2. Lewis, T. (1932). "Some special solutions of the equations of axially symmetric gravitational fields". Roy. Soc., Proc. 136: 176–92. doi:10.1098/rspa.1932.0073.
3. Papapetrou, A. (1948). "A static solution of the equations of the gravitatinal field for an arbitrary charge-distribution". Proc. R. Irish Acad. A. 52: 11. JSTOR 20488481.
4. 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.