Penrose limits of inhomogeneous spacetimes, their diagonalizability, and twistors

Penrose limits are considered in spacetimes admitting two Abelian, spacelike Killing vectors in general nonvacuum as well as in particular in the presence of an electromagnetic field. This class of spacetimes includes inhomogeneous cosmologies as well as colliding plane gravitational and the corresponding field waves or matter. Following the work of Tod [Classical Quantum Gravity 37, 075021 (2020)] the conditions for diagonal Penrose limits are investigated in these backgrounds. The twistor equation is considered in these spacetimes, and solutions are given in the radial Penrose limit.