Interpretation of the Weyl tensor

Understand

According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming and outgoing wavelike field components.

• It is shown here that this one-to-one correspondence does not hold for space-time geometries with cylindrical isometries.
• This is done by investigating some well-known exact solutions of Einstein's field equations with whole-cylindrical symmetry, for which the physical interpretation is very clear, but for which the standard Weyl interpretation would give contradictory results.
• For planar or spherical geometries, however, the standard interpretation works for both, static and dynamical space-times.