A tensorial approach to a beyond-GR Modified Teukolsky Equation

The increasing precision of gravitational wave detectors has enabled even more precise tests of general relativity, including spectroscopic tests of black holes through the measurement of their quasinormal modes (QNMs). These spectroscopic tests ideally compare the QNM frequencies to predictions from theories beyond GR, where the lack of a separable wave equation prevents computing quasinormal modes. We approach this problem by directly analyzing the tensorial form of the equations of motion in general beyond-GR theories, then later projecting to a new shifted Teukoslky equation. We also show how this can be used to compute the shifts in the gravitational ringdown spectrum in beyond-GR theories.