Weyl–Lewis–Papapetrou coordinates

Details

The square of the line element is of the form:

${\displaystyle d{s}^2=-e^{2\nu }d{t}^2+{\rho }^2{B}^2{e}^{-2\nu }(d\varphi -\omega dt{)}^2+e^{2(\lambda -\nu )}(d{\rho }^2+d{z}^2)}$

where ${\displaystyle (t,\rho ,\varphi ,z)}$ are the cylindrical Weyl–Lewis–Papapetrou coordinates in ${\displaystyle 3+1}$-dimensional spacetime, and ${\displaystyle \lambda }$, ${\displaystyle \nu }$, ${\displaystyle \omega }$, and ${\displaystyle B}$, are unknown functions of the spatial non-angular coordinates ${\displaystyle \rho }$ and ${\displaystyle z}$ only. Different authors define the functions of the coordinates differently.