Weyl–Lewis–Papapetrou coordinates
# Weyl–Lewis–Papapetrou coordinates

General relativity :

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

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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.

## Details

The square of the line element is of the form:

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

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.

