Ring-down gravitational waves and lensing observables: How far can a wormhole mimic those of a black hole?

It has been argued that the recently detected ring-down gravity waveforms could be indicative only of the presence of light rings in a horizonless object, such as a surgical Schwarzschild wormhole, with the frequencies differing drastically from those of the horizon quasinormal mode frequencies ${\ensuremath{\omega}}_{\mathrm{QNM}}$ at late times. While the possibility of such a horizonless alternative is novel by itself, we show by the example of the Ellis-Bronnikov wormhole that the differences in ${\ensuremath{\omega}}_{\mathrm{QNM}}$ in the eikonal limit (large $l$) need not be drastic. This result will be reached by exploiting the connection between ${\ensuremath{\omega}}_{\mathrm{QNM}}$ and the Bozza strong field lensing parameters. We shall also show that the lensing observables of the Ellis-Bronnikov wormhole can be very close to those of a black hole (say, $\text{Sgr}{\mathrm{A}}^{*}$ hosted by our galaxy) of the same mass. This situation indicates that the ring-down frequencies and lensing observables of the Ellis-Bronnikov wormhole can remarkably mimic those of a black hole. The constraint on wormhole parameter $\ensuremath{\gamma}$ imposed by experimental accuracy is briefly discussed. We also provide independent arguments supporting the stability of the Ellis-Bronnikov wormhole proven recently.