Quasi-normal modes and shadows of scale-dependent regular black holes

TL;DR

This paper explores the properties of a scale-dependent regular black hole by analyzing its quasi-normal modes and shadows, revealing how the extra parameter influences its response to perturbations and imaging features, and confirming a strong correspondence between modes and photon orbits.

Contribution

It introduces a detailed study of how a scale-dependent parameter affects black hole perturbations and shadows, and confirms the accuracy of the quasi-normal mode and photon orbit correspondence.

Findings

The parameter $psilon$ significantly influences quasi-normal mode frequencies.

The black hole shadow size varies with $psilon$ and can be accurately predicted from quasi-normal modes.

The correspondence between quasi-normal modes and unstable photon orbits is highly accurate for large multipole numbers.

Abstract

In this paper we investigate how a regular scale-dependent black hole, characterized by a single extra parameter $\epsilon$, behaves under perturbations by a test field (quasi-normal modes) and under light imaging (shadows) in a four-dimensional space-time background. On the quasi-normal modes side, we study how it responds to scalar and Dirac perturbations. To do this, we implement the well known WKB semi-analytic method of 6th order for obtaining the quasi-normal frequencies. We discuss the behavior of the real and imaginary parts of the quasi-normal modes for different values of the parameter $\epsilon$ and the overtone $n$ and multipole $\ell$ numbers. On the black hole imaging side, we ray-trace the geometry and illuminate it with a thin-accretion disk. Choosing $\epsilon=1.0$ we compute the size of the central brightness depression and generate full images of the black hole. We discuss the features (i.e. luminosity) of successive photon rings through the Lyapunov exponent of nearly-bound, unstable geodesics. Furthermore we use the correspondence (in the limit $\ell \gg n$) between quasi-normal mode frequencies and unstable bound light orbits to infer the numerical values of the latter using the former and find a remarkable accuracy of the correspondence in providing the right numbers. Our results support the usefulness of this correspondence in order to perform cross-tests of black holes using these two messengers.