We present a systematic construction of the Penrose coordinates and plane wave limits of spacetimes for which both the null Hamilton-Jacobi and geodesic equations separate. The method is illustrated for the Kerr-NUT-(A)dS four-dimensional black holes. The plane wave limits of the near horizon geometry of the extreme Kerr black hole are also explored. All near horizon geometries of extreme black holes with a Killing horizon admit Minkowski spacetime as a plane wave limit.
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