Speaker
Description
Black-hole ringdown provides a promising way to test deviations from the Kerr geometry, especially when compact objects are surrounded by matter fields or effective hair. In this work, we study how small deviations from Schwarzschild and Kerr spacetimes modify the eikonal quasinormal-mode spectrum through the properties of unstable circular null geodesics. We derive first-order shifts in the orbital frequency and Lyapunov exponent associated with the photon ring, allowing the real and imaginary parts of the ringdown frequency to be connected directly to perturbations of the background geometry.
We apply this framework to representative regular and matter-supported black-hole models, including Bardeen, Hayward, and Kiselev-type geometries, and compare the perturbative predictions with numerical geodesic calculations. In the rotating case, we analyse the equatorial co-rotating and counter-rotating sectors, where the azimuthal harmonic number selects the corresponding null orbit. We also discuss the scope of the eikonal correspondence in non-vacuum spacetimes and its limitations for interpreting ringdown observables.
This approach provides a compact diagnostic for identifying matter-induced deviations in black-hole ringdown. It offers a bridge between geodesic observables, photon-ring structure, and gravitational-wave tests of compact objects beyond Kerr.