A key virtue of splitting spacetime according to the 2+2 scheme is its
flexibility. It accommodates the necessary Rindler coordinate
geometries which are called for by the physical problem: accelerated
frames for the accelerated sources, and expanding inertial frames for
the inertial observers who measure the radiation emitted from these
sources. These geometries are

and

In these two frames the Rindler/polar-coordinatized version of Eq.(5) is

and

The feature common to the T.E. and the T.M. field is that both
of them are based on the two-dimensional curl of a scalar, say .
The difference is that for the T.E. field this curl is in the Euclidean plane,

while for the T.M. field this curl is the Lorentz plane,

and

The and are the components of the antisymmetric area tensors on the two respective planes.