What Singularity-Free Black Holes Hide express
Ordinary black holes hide a point of infinite density inside — a singularity, where physics breaks down. But some models replace it with a dense, yet finite core. From the outside, they're almost indistinguishable, and astrophysicists are looking for a way to probe the truth. Weak light bending from distant stars — like a palm feeling a shape — gives only a blurry picture. Direct images of the shadow, however, are a clear silhouette, and from it we can measure the core with surprising accuracy.
But even a sharp shadow doesn't always reveal the secret: geometry hides microscopic details, just as a shell prevents you from tapping out the filling. To hear the ring or the thud, scientists catch gravitational waves — ripples in space from the hole's vibrations — and analyze light delays near the horizon. An unexpected fact: in infalling gas, when the flow regime changes, the brightness rearranges itself, as if a familiar rhythm stumbles — and gives away the core's secret.
These signals will help us understand whether there's an abyss or a bridge. The first model of a regular black hole appeared in 1968, long before any images, and now it can be tested.
Original abstract
as written by the authors arXiv:2603.20596
We examine parameter degeneracies in Culetu, Bardeen and Hayward regular black holes across lensing, shadow and quasinormal mode regimes. Our analysis reveals that while Einstein ring data yield extremely loose constraints, with the regularization parameter $$q$$ exceeding $$\mathcal{O}(10^3)$$, they fail to improve the parameter estimation when combined with strong lensing observables. In contrast, the Event Horizon Telescope observations provide remarkably tight limits: $$0 \leq q < 0.0466 <0.0847$$ for Culetu, $$0 \leq q < 0.5115 <0.6682$$ for Bardeen and $$0 \leq q < 1.0258 <1.1881$$ for Hayward, which shows that the strong field regime alone dominates the available parameter space. Despite these bounds, leading order geometric observables remain highly degenerate, which masks the microscopic details of non-singular cores. To break this ``macroscopic universality,'' we identify high order signatures, such as the Lyapunov exponent and subleading time delays, as sensitive probes of near horizon curvature. Crucially, we discover that the brightness hierarchy of accretion induced intensity profiles undergoes a fundamental inversion when transitioning from lensing dominated static flows to dynamics dominated infalling flows. These results demonstrate that high resolution temporal and intensity profiles are essential for distinguishing between regular black hole geometries.
The first model of a singularity-free black hole appeared in 1968, long before an image of its shadow.
Non-singular black holes resemble portals from science fiction stories — inside, there's no point of crushing infinity.