The motivation comes from one of the deepest puzzles in theoretical physics. Hawking radiation, the faint quantum glow predicted to escape from black holes, appears to carry no information about what fell in, threatening the foundations of quantum mechanics. One radical proposal to avoid this information loss is to abandon the equivalence principle near the horizon, replacing the smooth spacetime of Einstein’s theory with a firewall of high-energy particles. Related ideas suggest that quantum gravity effects could replace the horizon with a hard or reflective surface. In such a picture, the objects we observe would be black hole mimickers — horizonless compact objects such as gravastars, boson stars or other exotic configurations that look almost identical to black holes from a distance but possess a physical surface capable of reflecting radiation.

Distinguishing these mimickers from genuine black holes observationally is notoriously difficult. The LIGO–Virgo–KAGRA collaboration has confirmed the existence of astrophysical black holes through gravitational waves, and the Event Horizon Telescope has imaged the horizon-scale shadow of the supermassive black hole in M87, including its polarized ring that traces the magnetic field structure near the horizon. Yet none of these landmark results has fully ruled out horizonless alternatives. The Czech team’s approach targets a different observable: the timing of electromagnetic radiation from a hot spot, a localized blob of hot plasma orbiting in the accretion flow. Hot spots are not hypothetical — the GRAVITY Collaboration has detected orbital motion of a compact emission region near the last stable orbit around Sagittarius A*, the black hole at the center of our own galaxy, igniting intense interest in modeling such sources.

The researchers modeled an isolated, geometrically thin and optically thick hot spot on a circular Keplerian orbit in the equatorial plane of a Kerr black hole, the rotating solution of general relativity that describes all known astrophysical black hole candidates. Their key modification is a perfect mirror placed at a radius just above the event horizon, at a depth parameter epsilon above the horizon radius. The mirror does not alter the underlying spacetime; it simply reflects photons that would otherwise be lost forever. Photons striking the mirror conserve energy and angular momentum, with the reflection performed in the locally non-rotating frame before transforming back to the global coordinates, a technique that keeps the calculation physically consistent in the strongly curved region near the horizon.

To compute what a distant observer would actually see, the team employed backward ray tracing. Starting from a two-dimensional photographic plate at the observer’s location, they divided the sky into pixels and traced each photon’s geodesic backward into the Kerr spacetime, using the constants of motion derived from the Hamilton–Jacobi separation of the photon equations. Along each ray they recorded where it intersects the equatorial plane, the emission radius, and the frequency shift factor that combines gravitational redshift and relativistic Doppler effects. The hot spot’s brightness follows a Gaussian profile centered on its orbital position, and the observed flux in each time bin accumulates the contributions of all photons, weighted by the fourth power of the frequency shift factor — a factor that accounts for photon energy shifts, time dilation of the arrival rate, and relativistic corrections to the solid angle.

The simulations reveal a clear signature. In the standard Kerr picture, photons emitted inward from the hot spot simply plunge through the horizon and vanish. With a mirror present, those photons reflect and a fraction climb back out to the observer, arriving long after the primary emission has faded. For lower black hole spins, the round-trip delay to the mirror and back is shorter than the orbital period, so the reflected photons arrive within the same orbital cycle and produce a noticeable enhancement of the flux. For higher spins, the innermost stable circular orbit — where the team places the hot spot to maximize the effect — moves closer to the horizon, deepening the effective potential well and stretching the photon’s journey. The echo then emerges only after several orbits, leaving a characteristic echo wave train trailing the primary light curve once the hot spot ceases to exist.

The timing structure depends delicately on three parameters: the black hole spin, the mirror depth, and the orbital radius of the hot spot. The researchers derived an analytic expression for the echo delay of a zero-angular-momentum photon traveling radially from the emitter to the mirror and back, and compared it with the orbital period at each radius. For a spin of half the maximum and a mirror depth of one hundred-thousandth of the gravitational radius, the echo delay always remains shorter than the orbital period, guaranteeing same-orbit returns. For nearly extremal spin, the situation flips: close to the innermost stable orbit the delay is marginally shorter than the orbital period, but at larger radii it exceeds it, so reflected photons from early emission are detected only after the hot spot has completed additional revolutions. In some configurations the two timescales become nearly equal near one and a half times the innermost stable orbit, producing an overlap between direct and reflected contributions within a single cycle — a marginal case that would appear as a distinctive distortion of the light curve.

Crucially, the team also assessed whether such echoes could realistically be detected. Taking the NuSTAR X-ray observatory, with a flux sensitivity of roughly ten to the minus fourteen ergs per square centimeter per second, they considered a ten-solar-mass black hole accompanied by a plasma ball of effective temperature around ten million kelvin and radius about a tenth of the gravitational radius, located one kiloparsec away. The primary flux in this scenario is around ten to the minus eight ergs per square centimeter per second, and detectability requires the echo to be no more than a million times fainter than the primary signal. In their simulations the ratio between primary and echoed flux lies between roughly twenty and eighty — comfortably within reach. The authors also note that a neutron star of the same mass, whose surface sits farther out and therefore intercepts several times more incident radiation, would produce an even stronger reflected component, though modeling its atmosphere requires separate assumptions about stellar structure.

The study is candid about its limitations. The toy model assumes a perfect mirror, a hot spot confined to the equatorial plane on a circular geodesic, and isotropic emission, while real photons with non-zero angular momentum will trace more complex paths and modify the detailed shape of the echo. The flux enhancement is also modest, so it may be hard to disentangle when a hot spot persists on a stable orbit for a long time; transient hot spots that form and dissipate on short timescales, or a star spiraling down and ultimately colliding with the mirror, could make the effect far more dramatic. The authors flag these dynamical scenarios for future work, along with a full treatment of hot spots in general orbits to determine whether current facilities could catch the signature.

Even so, the qualitative picture is robust and potentially transformative. Just as gravitational wave echoes have been proposed as a test of Planck-scale structure at black hole horizons, these electromagnetic echoes would encode the geometry of the region immediately outside the horizon: the deeper the mirror, the longer the delay, and the faster the spin, the later and more extended the echo train. Next-generation instruments — the Einstein Telescope and Cosmic Explorer in gravitational waves, the LISA space mission, and upgraded Event Horizon Telescope arrays — are expected to push strong-field gravity tests to unprecedented precision. If a mirror-like surface truly screens the horizons of some compact objects, the light from orbiting hot spots may already carry the telltale delayed heartbeat of a black hole impostor, waiting in the timing residuals of future X-ray observations to be read.

Subject of Research: Electromagnetic echo signatures from hot spots orbiting Kerr black hole mimickers with reflective surfaces near the horizon

Article Title: Timing of echoes in electromagnetic radiation from hot spots orbiting a Kerr black hole impostor

Article References: Hensh, S., Schee, J., & Stuchlík, Z. (2026). Timing of echoes in electromagnetic radiation from hot spots orbiting a Kerr black hole impostor. The European Physical Journal C, 86(9), Article 1040. https://doi.org/10.1140/epjc/s10052-026-16312-9

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16312-9

Keywords: black holes, black hole mimickers, event horizon, Kerr spacetime, hot spots, light curves, ray tracing, echoes, gravastars, boson stars, accretion disks, strong-field gravity