In general relativity, the Weyl–Lewis–Papapetrou coordinates are used in 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]

This article may be too technical for most readers to understand. (October 2013)

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 ${\displaystyle (t,\rho ,\phi ,z)}$ 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.

• Introduction to the mathematics of general relativity
• Stress–energy tensor
• Metric tensor (general relativity)
• Relativistic angular momentum
• Weyl metrics