Quasinormal modes of Kerr-like black bounce spacetime

TL;DR

This paper analyzes the quasinormal-mode spectrum of a Kerr-like black-bounce spacetime under massive scalar perturbations. By deriving the separated radial and angular equations from a Newman–Janis generated metric with bounce parameter $p$, the authors cast the radial part into a Schrödinger-like form with a double-peaked $V_{eff}$, signaling potential echoes. They compute QNM frequencies via the Pöschl–Teller approximation and sixth-order WKB, finding good agreement and showing systematic decreases in both oscillation frequency and damping as $a$ and $p$ grow, with significant shifts induced by the scalar mass $\\mu$. These findings suggest observable imprints in ringdown signals and motivate future time-domain analyses and gravitational perturbation studies to test rotating black-bounce geometries with current and upcoming detectors such as LIGO/Virgo and LISA.

Abstract

We investigate the quasinormal mode (QNM) spectrum of a Kerr-like black-bounce spacetime under massive scalar-field perturbations. Starting from the Kerr-like deformation of the Simpson--Visser black-bounce geometry, we derive the corresponding radial and angular equations and obtain the effective potential governing scalar perturbations. We show that the Kerr-like black-bounce spacetime inherits a characteristic double-peaked effective potential, analogous to the Schwarzschild-like black-bounce case, which is known to be associated with late-time echo signals. The QNM frequencies are computed by means of the Pöschl--Teller potential approximation and the semi-analytic WKB method (up to sixth order), and we demonstrate good agreement between these two approaches. We then analyze in detail how the QNM spectrum depends on the spin parameter $a$, the bounce parameter $p$ that interpolates between black-hole and wormhole geometries, and the scalar-field mass $μ$. Our results indicate that increasing either $a$ or $p$ lowers both the real frequency and the magnitude of the imaginary part, leading to longer-lived modes. Moreover, the mass of the scalar field has a non-negligible impact on the ringdown spectrum. These features suggest that rotating black-bounce geometries may leave distinct imprints in the ringdown phase of gravitational-wave signals, and motivate future studies of echoes and parameter estimation in the context of present and upcoming detectors.

Figures (6)

• Figure 1: Effective potential $V_{eff}$ under the Kerr-like black bounce space-time scalar perturbation for different $a$ with $p=1,m=1,M=1,\mu=0.5,\Lambda_{lm}=2$.
• Figure 2: Effective potential $V_{eff}$ under the Kerr-like black bounce space-time scalar perturbation for different $\Lambda_{lm}$ with $a=0.3,p=1,m=1,M=1,\mu=0.5$.
• Figure 3: Effective potential $V_{eff}$ under the Kerr-like black bounce space-time scalar perturbation for different $p$ with $a=0.3,m=1,M=1,\mu=0.5,\Lambda_{lm}=2$.
• Figure 4: Frequency spectrum of scalar perturbation of rotating black bounce space-time for different $a$ with $m=1,M=1,p=1,\Lambda_{lm}=2$. The top panel is the oscillation frequency Re$\omega$/$\mu$, and bottom panel is the damping rate Im$\omega$/$\mu$, as the function of mass $\mu$.
• Figure 5: Frequency spectrum of scalar perturbation of rotating black bounce space-time for different $\Lambda_{lm}$ with $a=0.1,m=1,M=1,p=0.5$. The top panel is the oscillation frequency Re$\omega$/$\mu$, and bottom panel is the damping rate Im$\omega$/$\mu$, as the function of mass $\mu$.