IAS Amplitudes Group Meeting

Abstract: We present a unified geometric perspective on the symmetries underlying the spin 0, 1, and 2 static perturbations around a Schwarzschild black hole. The symmetries are exact, each forming an SO(3,1) group. They can be formulated at the level of the action, provided the appropriate field variables are chosen. For spin 1 and 2, the convenient variables are certain combinations of the gauge fields for even perturbations, and dual scalars for odd perturbations. The even and odd sector each has its own SO(3, 1) symmetry. In addition, there is an SO(2) symmetry connecting them, furnishing an economical description of Chandrasekhar's duality. Our formulation makes it possible to state the symmetries responsible for the vanishing of the Wilson coefficients characterizing the spin 0, 1, and 2 static tidal response, in the effective point particle description of a black hole. We discuss the connections between these geometric symmetries and ladder symmetries connecting solutions of the equations of motion. We also discuss extensions to Kerr black holes and higher dimensional black holes.