From Ringdown to Lensing: Analytic Eikonal Modes of Quasi-Topological Regular Black Holes

Abstract

We develop an analytic eikonal description of perturbations for four-dimensional regular black holes in quasi-topological gravity. Using first-order Schutz--Will WKB together with a small-coupling expansion and a large-$\ell$ expansion, we obtain closed quasinormal-mode formulas with explicit dependence on the black-hole parameters $(M,\hat{I}¼,\hat{I}½,\hat{I}\pm )$. We then map the same geodesic invariants $(\hat{I}{\text{c◯}}_{\text{ph}},\hat{I}{»}_{\text{ph}})$ to shadow and strong-lensing observables, deriving an explicit QNM--shadow--lensing correspondence. In this way, ringdown frequencies, shadow scale, and strong-deflection observables are unified in one analytic scheme for this quasi-topological family.