Can wormholes mirror the quasi-normal mode spectrum of Schwarzschild black holes?

Abstract: Wormholes are exotic compact objects characterized by the absence of essential singularities and horizons, acting as slender bridges linking two distinct regions of spacetime. Despite their theoretical significance, they remain however undetected, possibly due to their ability to closely mimic the observational properties of black holes. This study explores whether a static and spherically symmetric wormhole within General Relativity can reproduce the quasi-normal mode spectrum of a Schwarzschild black hole under scalar, electromagnetic, and axial gravitational perturbations, both individually and in combination. To address this, we reformulate the wormhole metric components using a near-throat parametrization. Our analysis concentrates on the fundamental mode and first overtone, estimated via the Wentzel-Kramers-Brillouin method. By employing a customized minimization strategy, we demonstrate that within a specific region of the parameter space, a wormhole can successfully replicate a subset of the black hole quasi-normal mode spectrum.