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

TL;DR

This paper presents an analytic framework linking quasinormal modes, shadow, and lensing observables for regular black holes in quasi-topological gravity, enabling unified analysis of these phenomena.

Contribution

It introduces a novel analytic eikonal approach that connects black hole perturbations with observational signatures in a unified manner.

Findings

Derived explicit formulas for quasinormal modes with black-hole parameters.

Established a direct correspondence between QNM frequencies and lensing/shadow observables.

Unified description of ringdown, shadow, and lensing in a single analytic scheme.

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 $(M,\mu,\nu,\alpha)$. We then map the same geodesic invariants $(\Omega_{\text{ph}},\lambda_{\text{ph}})$ 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.