# 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, T. Lewis, and Achilles Papapetrou.

The square of the line element is of the form:[1]

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

where (tρϕz) 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.

## References

1. ^ 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.