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Algebraic and Optical Classification of Generalized Kerr-Schild Spacetimes in Higher Dimensions

How generalized Kerr-Schild metrics - a background metric deformed along a null direction - behave in arbitrary dimension: when the null vector is geodesic, how the algebraic types of the Ricci and Weyl tensors of the full and background geometries constrain each other, and what the optical scalars must satisfy. Students learn why these spacetimes need not be algebraically special and how the vacuum case connects to Robinson-Trautman solutions.