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Gravitational shockwaves on rotating black holes

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Gravitational shockwaves may signal the breakdown of effective field theory near black hole horizons. Motivated by this, I will revisit the Dray-‘t Hooft solution and explain how to generalize it to the Kerr-Newman background. In doing so I will emphasize the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).