Equatorial and polar quasinormal modes and quasiperiodic oscillations of quantum deformed Kerr black hole

TL;DR

This paper investigates the quasinormal modes and shadow properties of a quantum deformed Kerr black hole, revealing relations between modes, orbits, and stability, with implications for astrophysical observations.

Contribution

It introduces a detailed analysis of QNMs and shadows for quantum deformed Kerr black holes, linking modes to geodesic parameters and exploring astrophysical applications.

Findings

Real part of QNMs relates to Keplerian frequency in the eikonal limit

Derived shadow radius relations for different viewing angles

Assessed thermodynamical stability and astrophysical constraints

Abstract

In this paper we focus on the relation between quasinormal modes (QNMs) and a rotating black hole shadows. As a specific example, we consider the quantum deformed Kerr black hole obtained via Newman--Janis--Azreg-A\"{\i}nou algorithm. In particular, using the geometric-optics correspondence between the parameters of a QNMs and the conserved quantities along geodesics, we show that, in the eikonal limit, the real part of QNMs is related to the Keplerian frequency for equatorial orbits. To this end, we explore the typical shadow radius for the viewing angles, $\theta_0=\pi/2$, and obtained an interesting relation in the case of viewing angle $\theta_0=0$ (or equivalently $\theta_0=\pi$). Furthermore we have computed the corresponding equatorial and polar modes and the thermodynamical stability of the quantum deformed Kerr black hole. We also investigate other astrophysical applications such as the quasiperiodic oscillations and the motion of S2 star to constrain the quantum deforming parameter.