When a static, spherically symmetric configuration approaches a marginal-trapping threshold, it develops a long throat: the nondegenerate minimum of F = 1 − 2m/r tends to zero as F ≃ Δ + β(r − R_M)², and the proper length across the throat grows as −ln Δ/√β even though the local curvature remains finite. A new study examines how axial gravitational waves propagate in an effective model of this throat, with the lapse parametrized as N ∝ F^(s/2), and finds that for s > 0 the throat acts as a cavity behind the angular-momentum barrier.

Waves reflected from that cavity reappear as echoes spaced by T_echo ≃ 2Λ + δ ∝ Δ^(−s/2), where Λ is the optical length of the throat and δ does not depend on Δ. The authors apply this scheme to four-dimensional, matter-supported quasi-black holes in which a regular centre caps the near-AdS₂ throat, a simplified model of horizonless microstate geometries. The echo delay is controlled by the inverse redshift near the bottom of the throat, unlike thin-shell gravastars and wormholes, where the delay grows only logarithmically with the distance to the would-be horizon.

Time-domain evolutions confirm the Δ^(−s/2) scaling over three decades in Δ; for s = 0 the throat becomes part of the barrier and no distinct echo appears. The barrier also imposes a greybody cutoff on the reflected spectrum, 1 − Γ ≃ e^(−(ω − f)/T), with T fixed by the curvature of the barrier and independent of the surface gravity of any horizon behind it. In this model the prompt signal is the same whether the interior contains a horizon or a reflecting throat, but in the horizonless case the transmitted wave returns as echoes, restoring the high-frequency part of the full reflected spectrum.