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.