At the center of an ordinary black hole, according to classical ideas, lurks a singularity — a point of infinite density where the laws of physics break down. But some theories, inspired by the duality idea from string theory, propose replacing the point with a tiny 'smudged' region. Its size is set by the so-called zero-point length (the minimal possible distance below which space loses meaning).
The authors took such a nonsingular black hole and looked at how it affects two familiar physical phenomena: the 'ringing' of a massive scalar field (ripples you could compare to the echo of a struck bell) and the motion of particles and light near the horizon. Gravitational waves aren't directly involved here, but the approach resonates with their analysis.
What did they find? On one hand, the heavier the scalar field, the higher its oscillation frequency and the slower it decays, such a long ring could become a noticeable signature of such objects. On the other hand, the larger the zero-point length, the smaller the black hole's shadow becomes (that dark silhouette against the bright accretion disk), the photon ring frequency increases, and the binding energy on circular orbits grows. In other words, the same regularization leaves consistent imprints in both the wave echo and the shadow geometry.
If our Sun were compressed into a black hole, its event horizon would be only about 6 kilometers across, and the zero-point length in question is billions upon billions of times smaller than a proton.
In Greg Egan's novel 'The Light of Distant Stars', universes with modified gravity are explored, where familiar astrophysical objects behave differently, and black hole shadows can differ greatly from Einstein's predictions.