Branch-dependent ringdown in black-bounce spacetimes: imprints of matter-source ambiguity on quasinormal modes

Abstract

Regular black holes and black-bounce spacetimes frequently emerge in theoretical frameworks beyond general relativity, as well as in general relativity coupled to non-linear sources. A profound complication in these frameworks is source ambiguity: a single spacetime metric can often be supported by multiple, inequivalent matter-source interpretations, such as an anisotropic fluid or nonlinear electrodynamics (NED) coupled to a scalar field. We investigate how this fundamental degeneracy dynamically imprints on axial gravitational perturbations within the Simpson-Visser spacetime, which smoothly transitions from a regular black hole (BH) to a traversable wormhole (WH) at a critical bounce parameter $a=2M$. By deriving the exact master equations for each interpretation, we perform time-domain numerical evolutions to extract the quasinormal modes (QNMs) via Prony fitting. In the BH branch ($a\le2M$), the NED interpretation exhibits faster QNM damping than the fluid model, driven by enhanced energy leakage through the coupled electromagnetic channel alongside horizon absorption. Conversely, in the WH branch ($a>2M$), the NED coupled system produces longer-lived fundamental modes. This reduced damping is governed by subradiant-like interference that actively suppresses radiative losses to the two asymptotically flat regions. This branch-dependent dynamics, analogous to decay-width redistribution in open non-Hermitian quantum systems, demonstrates that matter-source ambiguity leaves distinct, observable signatures in ringdown waveforms. Our findings establish that gravitational-wave spectroscopy can systematically break the degeneracy of source interpretations, providing a novel empirical pathway to probe the physical nature of exotic compact objects.

Figures (3)

• Figure 1: QNM spectra as functions of the bounce parameter $a$ (in units of $M$, $l=2$) for the four mode families: AF (solid red), NED GR-led (dashed blue), EM (solid green), and NED EM-led (dotted purple). The vertical gray band indicates the geometric transition at $a=2M$. Panels \ref{['fig:qnms_a_real']}, \ref{['fig:qnms_a_imag']}, and \ref{['fig:qnms_a_loss']} display the real part, imaginary part, and loss tangent ($|\Im(\omega)|/\Re(\omega)$) of the fundamental frequencies, respectively.
• Figure 2: Trajectories of the QNM frequencies in the complex plane as the bounce parameter $a$ varies across the BH-WH transition ($l = 2$). Panel \ref{['fig:qnms_complex_combined']} shows the combined spectral trajectories for all four mode families. Panel \ref{['fig:qnms_complex_argand']} presents the corresponding Argand diagram, colored continuously by $a$, illustrating the avoided-crossing dynamics. Filled circles and squares mark the endpoints at the minimum and maximum surveyed values of $a$, respectively.
• Figure 3: Time-domain ringdown waveforms of $-7.7\,H_1$ (orange dashed) and $H_2$ (blue) in the WH branch, extracted at a fixed observation point. The two channels oscillate in near-perfect anti-phase at identical frequencies, demonstrating the mode locking of Eq. \ref{['eq:modelocking']}.