where n is the refractive index. This is analogous to Kerr-Schild form, which uses a null vector field in place of timelike. An open question is which spacetimes can be expressed in this way. The challenge is to pick coordinate systems for which the above relationship holds. Schwarzschild spacetime, which describes a non-rotating black hole, can be expressed this way. There has been progress for Kerr spacetime which describes a rotating black hole, but this case remains elusive.