Since 2015, the LIGO, Virgo, and KAGRA detectors have been registering gravitational waves from mergers of compact objects, and each signal is a test of general relativity in the strong-field regime. Among alternatives to classical black holes, there is a whole zoo of horizonless objects: gravastars, boson stars, quantum black holes, and fuzzballs. All of them are almost indistinguishable from black holes in mass and size, but they lack a horizon; instead, they have a reflective surface at a distance rs=2M(1+ε), where ε can be arbitrarily small, down to the Planck length. Reflection of waves from this surface changes the system's response, and the challenge is to find an observable signature that cannot be confused with a black hole. This work belongs to a line of research seeking such signatures through quasinormal modes, tidal deformations, and echo signals, but it proposes a new tool: the spectrum of the plunge itself, not just the ringdown phase.
Instead of a full merger, the extreme mass ratio is considered: a light particle (mass μ) falls onto a massive object (mass M), with μ≪M. After the last stable circular orbit, the particle transitions into a geodesic plunge, and its trajectory is described by the geodesic equations in the Schwarzschild field. To obtain analytical control, the authors use a surrogate model: a direct radial or non-radial plunge from infinity instead of a plunge from the last stable orbit. Metric perturbations are described by the Regge–Wheeler and Zerilli equations, with the source being a point particle. The reflective surface is imposed via a boundary condition with reflection coefficient R. The energy spectrum dE/dω is computed numerically via the Green's function: an integral of the source multiplied by homogeneous solutions, normalized by the Wronskian. Calculations are performed for the (ℓ,m)=(2,2) mode at different values of R (from 1 to 10⁻³) and ε (from 10⁻⁴ to 10⁻¹⁰), as well as for nonzero angular momentum up to 99% of the critical value.
The numerical analysis confirmed two predicted signatures. At low frequencies, the spectrum contains a comb of resonances at the real parts of the imitator's quasinormal modes, with spacing δω=π/(2M|log ε|). These resonances are analogous to those previously found in the inspiral phase, but now they are also visible in the plunge spectrum. The main result is that above the threshold Mωth≈0.39 (for the dominant mode), the spectrum qualitatively breaks down: for a black hole it decays exponentially, while for an imitator an additional contribution appears, proportional to |R|². At R=1 and Mω≈0.7, the energy exceeds the black-hole value by orders of magnitude. The high-frequency excess tail is described by the form $A_m$ $e^{-k_m ω}$, where $A_m$∝|R|², and is almost independent of the surface position ε. This behavior is reproduced for nonzero angular momentum: the tail is nearly universal, weakly dependent on L, which strengthens confidence in the surrogate model. Additionally, it is shown that the gray factor (the transmission coefficient through the potential barrier) approaches unity above the threshold, which physically explains the excess: waves pass through the barrier, reflect off the surface, and return to the observer.
This work adds a new, independent channel to the arsenal of horizon tests: the plunge spectrum. Unlike neighboring works that focus on resonances in the inspiral or echoes in the ringdown phase, here the entire frequency range excited by non-monochromatic fall is used. This allows probing beyond the ωISCO threshold, inaccessible in quasi-circular inspiral, and directly sampling the region near the horizon. The high-frequency excess turns out to be robust to details of the source and the surface position, making it a reliable signature of the absence of a horizon. Although a single plunge in an extreme-mass-ratio event gives a low signal-to-noise ratio, coherent stacking of many events could make the signature detectable.
The next step is a full time-domain analysis of the plunge–merger–ringdown waveform for imitators, with proper treatment of the source after crossing the surface. This will require careful windowing methods to avoid artifacts from source truncation. Another direction is generalization to a geodesic plunge from the last stable orbit (GUI) instead of the surrogate direct fall, as well as to rotating objects. For observations, the key task is to develop a strategy for coherent stacking of signals from many LISA events, including accurate modeling of the inspiral–plunge transition phase.
The result directly affects LISA observation planning and the interpretation of future extreme-mass-ratio data. It also provides a new tool for testing quantum gravity models that predict reflective surfaces.
Construct full time-domain plunge waveforms for imitators and assess systematics. Develop a method for stacking signals from many events to improve signal-to-noise ratio.
In gravitational-wave physics, the nature of compact objects remains an open question: do all black hole candidates truly possess an event horizon? This work connects this problem to an observable quantity—the plunge spectrum—which can be measured by future detectors. The unresolved challenge of accurately modeling the inspiral-to-plunge transition for horizonless objects remains, which is necessary for practical signal stacking.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The paper examines the fall of a light object onto a supermassive compact object and computes the gravitational wave spectrum. The authors use an analytic surrogate model of a direct plunge and numerically solve the Regge–Wheeler and Zerilli equations with a reflective boundary condition. They show that black hole mimickers exhibit a comb of resonances at low frequencies and an excess of radiation above the threshold Mω≈0.39, proportional to the square of the reflection coefficient.
Where its strength is
A strong point is the identification of a universal high-frequency tail that is almost independent of the position of the reflecting surface and of the angular momentum, which makes it a reliable signature of a horizon.
Where it could go next
Worth trying
Why this may matter
If the proposed signature turns out to be observable, it would provide a direct test for the presence of a horizon in supermassive compact objects, which is important for fundamental physics and for understanding the nature of black holes.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.61, against a usual 0.64. It looks like few have drilled nearby.
The threshold Mωth≈0.39 almost coincides with the real part of the fundamental quasinormal mode of a Schwarzschild black hole. For a supermassive black hole with a mass of 10⁶ solar masses, this frequency falls into the most sensitive band of LISA, around 0.01 Hz.
The idea of a reflective surface instead of a horizon echoes Stanisław Lem's novel "Fiasco," where a black hole turns out to be not a bottomless pit but an object with nontrivial internal structure, and the film "Interstellar," where data from beyond the horizon is transmitted through quantum effects. In both cases, the horizon is not the end of physics but a door.