Pad\'e metrics for black hole perturbations and light rings

Most distinguishing features of black holes and their mimickers are concentrated near the horizon. In contrast, astrophysical observations and theoretical considerations primarily constrain the far-field geometry. In this work we develop tools to effectively describe both, using the two-point Pad\'e approximation to construct interpolating metrics connecting the near and far-field. We extend our previous work by computing the quasinormal modes of gravitational perturbations for static, spherically symmetric metrics that deviate from Schwarzschild spacetime. Even at the lowest order, this approach compares well with existing methods in both accuracy and applicability. Additionally, we show that the lowest-order interpolating metric reliably predicts light ring locations. It closely matches exact results, even when unsuitable for quasinormal frequency calculations.