# 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.[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 (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. ^ Weyl, H., "Zur Gravitationstheorie," Ann. der Physik 54 (1917), 117–145.
2. ^ T. Lewis, "Some special solutions of the equations of axially symmetric gravitational fields," Roy. Soc., Proc. 136, 176–92 (May 2, 1932).
3. ^ A. Papapetrou, "A static solution of the equations of the gravitatinal field for an arbitrary charge-distribution," Proc. R. Irish Acad. A 52, 11 (1948).
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.