Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework

Studies of quasinormal modes (QNMs) of black holes have a long and well-established history. Predominantly, much research in this area has customarily focused on the equations given by Regge, Wheeler, and Zerilli. In this work, we study linearized perturbations of a Schwarzschild black hole using the characteristic formulation of numerical relativity, with an emphasis on the computation of QNMs. Within this formalism, the master equation describing gravitational perturbations is known to satisfy a fourth-order differential equation. We analyze the singular points of this master equation, and obtain series solutions whose coefficients are given by three term recurrence relations, from which Leaver's continued fraction method can be applied. Using this technique, we recover the standard Schwarzschild quasinormal modes. In addition, we find that imposing purely outgoing boundary conditions, a natural feature of the Bondi-Sachs framework, leads to the recovery of the algebraically special mode.