Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale

TL;DR

The paper investigates gravitational-wave signatures of exotic compact objects (ECOs) and horizon-scale quantum corrections by analyzing (i) the universality of photon-sphere–driven ringdown for a broad ECO class, (ii) the late-time echoes produced by a PS cavity in wavepacket scattering, and (iii) head-on collisions of self-gravitating solitonic boson stars. It demonstrates that the initial ringdown can be BH-like, while horizon-scale corrections generate a train of modulated echoes with delay $\Delta t \sim -n M \log(\ell/M)$, where $\ell$ measures microscopic corrections; the echo structure is sensitive to the PS architecture and can be suppressed if PSs are absent. In BS collisions, BH formation occurs for sufficiently compact configurations, but the waveforms display distinctive pre-merger and scalar-field–driven features depending on phase relations, indicating potential smoking-gun ECO signals in some scenarios. Overall, the work argues that GW observations can both constrain ECO models and reveal quantum corrections at the horizon, provided accurate late-time templates and careful disentangling of PS-driven dynamics from genuine horizon- or environment-induced deviations.

Abstract

Gravitational waves from binary coalescences provide one of the cleanest signatures of the nature of compact objects. It has been recently argued that the post-merger ringdown waveform of exotic ultracompact objects is initially identical to that of a black-hole, and that putative corrections at the horizon scale will appear as secondary pulses after the main burst of radiation. Here we extend this analysis in three important directions: (i) we show that this result applies to a large class of exotic compact objects with a photon sphere for generic orbits in the test-particle limit; (ii) we investigate the late-time ringdown in more detail, showing that it is universally characterized by a modulated and distorted train of "echoes" of the modes of vibration associated with the photon sphere; (iii) we study for the first time equal-mass, head-on collisions of two ultracompact boson stars and compare their gravitational-wave signal to that produced by a pair of black-holes. If the initial objects are compact enough as to mimic a binary black-hole collision up to the merger, the final object exceeds the maximum mass for boson stars and collapses to a black-hole. This suggests that - in some configurations - the coalescence of compact boson stars might be almost indistinguishable from that of black-holes. On the other hand, generic configurations display peculiar signatures that can be searched for in gravitational-wave data as smoking guns of exotic compact objects.

Figures (7)

• Figure 1: Qualitative features of the effective potential felt by perturbations of a Schwarzschild BH compared to the case of wormholes Cardoso:2016rao and of star-like ECOs with a regular center Cardoso:2014sna. The precise location of the center of the star is model-dependent and was chosen for visual clarity. The maximum and minimum of the potential corresponds approximately to the location of the unstable and stable PS, and the correspondence is exact in the eikonal limit of large angular number $l$. In the wormhole case, modes can be trapped between the PSs in the two "universes". In the star-like case, modes are trapped between the PS and the centrifugal barrier near the center of the star 1991RSPSA.434..449CChandrasekhar:1992eyAbramowicz:1997qk. In all cases the potential is of finite height, and the modes leak away, with higher-frequency modes leaking on shorter timescales.
• Figure 2: Left: A dipolar ($l=1,m=0$) scalar wavepacket scattered off a Schwarzschild BH and off different ECOs with $\ell=10^{-6} M$ ($r_0=2.000001 M$). The right panel shows the late-time behavior of the waveform. The result for a wormhole, a gravastar, and a simple empty shell of matter are qualitatively similar and display a series of "echoes" which are modulated in amplitude and distorted in frequency. For this compactness, the delay time in Eq. \ref{['Deltat']} reads $\Delta t\approx 110 M$ for wormholes, $\Delta t\approx 82 M$ for gravastars, and $\Delta t\approx 55 M$ for empty shells, respectively.
• Figure 3: Left panel: The waveform for the radial infall of a particle with specific energy $E = 1.5$ into a wormhole with $\ell=10^{-6} M$, compared to the BH case. The BH ringdown, caused by oscillations of the outer PS as the particle crosses through, are also present in the wormhole waveform. A part of this pulse travels inwards and is absorbed by the event horizon (for BHs) or then bounces off the inner (centrifugal or PS) barrier for ECOs, giving rise to echoes of the initial pulse. This is a low-pass cavity which cleans the pulse of high-frequency components. At late times, only a lower frequency, long-lived signal is present, well described by the QNMs of the ECO. Right panel: the same for a scattering trajectory, with pericenter $r_{\rm min} = 4.3M$, off a wormhole with $\ell= 10^{-6} M$. The main pulse is generated now through the bremsstrahlung radiation emitted as the particle approaches the pericenter. The remaining main features are as before. We show only the real part of the waveform, the imaginary part displays the same qualitative behavior.
• Figure 4: GW signal produced by a test particle falling radially into a wormhole with $E=1.01$. We consider the same setup as in Ref. Cardoso:2016rao but for a wormhole without a PS. Without outer (and inner) PS, the ringdown signal is, clearly, different from that of a BH. Because there is no longer a good resonating cavity, echoes do not appear to be excited.
• Figure 5: Mass-radius relation for a solitonic BS with $\sigma_0=0.05m_P$. In the inset we show the compactness as a function of the central scalar field, $\sigma_c\equiv|\Phi(r=0)|$. The red and the green markers correspond, respectively, to the light BSs with $M/R\approx 0.118$ and to the medium-mass one with $M/R\approx 0.184$ whose numerical evolutions are discussed in the main text. The blue marker indicates a stable BS with nearly maximum mass and $M/R\approx 1/3$. The horizontal line in the right panel denotes the compactness of the Schwarzschild PS, $M/R=1/3$.