A geometric framework for black hole perturbations

Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the construction of short-ranged potentials for the perturbation equations in frequency domain.

Figure 1

Penrose diagram of the domain of outer communications in Schwarzschild spacetime depicting standard Schwarzschild time surfaces (dashed lines) and future horizon-penetrating, future hyperboloidal time surfaces (solid lines).