Raychaudhuri Equation - Optical Equations

Optical Equations

There is also an optical (or null) version of Raychaudhuri's equation for null geodesic congruences.

.

Here, the hats indicate that the expansion, shear and vorticity are only with respect to the transverse directions. When the vorticity is zero, then assuming the null energy condition, caustics will form before the affine parameter reaches .