Penrose limits onto the photon ring and past horizon of Schwarzschild produce pp-wave spacetimes whose isometries generate the evenly spaced overtones of eikonal and highly damped quasinormal modes.
Quasinormal modes and hidden conformal symmetry in the Reissner-Nordstrom black hole
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abstract
It is shown that the scalar wave equation in the near-horizon limit respects a hidden SL(2,R) invariance in the Reissner-Nordstrom (RN) black hole spacetimes. We use the SL(2,R) symmetry to determine algebraically the purely imaginary quasinormal frequencies of the RN black hole. We confirm that these are exactly quasinormal modes of scalar perturbation around the near-extremal black hole.
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pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes
Penrose limits onto the photon ring and past horizon of Schwarzschild produce pp-wave spacetimes whose isometries generate the evenly spaced overtones of eikonal and highly damped quasinormal modes.