A black hole is like a perfect vault: everything that falls in disappears without a trace. But in the 1970s, Jacob Bekenstein and Stephen Hawking discovered that the horizon carries an indelible "sticker" — entropy (a measure of hidden information about swallowed matter). It turned out to be proportional to the horizon's area, not its volume, as with ordinary bodies. This rule — the Bekenstein–Hawking law — became a cornerstone of black hole physics.
However, under extreme conditions where quantum effects become important, the simple area formula may break down. Corrections appear — logarithmic or power-law additions to entropy. The authors of the new study asked: can these corrections be detected from outside, without peering beneath the horizon? They showed that modified entropy drags the metric along — the mathematical description of spacetime curvature around the hole. And the metric, in turn, affects how light bends around the hole and what shadow we see.
The researchers calculated the photon sphere radius and shadow size for the corrected metric and compared them with the actual image of our galaxy's center — Sagittarius A* — obtained by the Event Horizon Telescope. It turned out that even small additions to entropy shift the shadow by an amount comparable to measurement precision. This allowed placing constraints on correction parameters: too strong deviations from the area law are simply incompatible with what we see.
Thus, the shadow of a black hole, frozen in a photograph, becomes a window into the world of quantum gravity. Like a barely visible scratch on a vault hints that the lock is more complex than it seemed.
as written by the authors arXiv:2605.01303
Starting from the first law of black hole thermodynamics, we establish an explicit correspondence between the corrected entropy and the metric function under the condition of fixed black hole energy and horizon position. Using the corrected metric, we further compute the photon sphere radius and shadow size, demonstrating that different entropy corrections lead to characteristic optical shifts. By comparing with the Event Horizon Telescope observations of Sgr A*, we constrain the parameter range introduced in the corrected entropy. This provides a feasible approach for testing generalized entropy frameworks and probing deviations from the Bekenstein-Hawking area law.
The entropy of a black hole with the mass of the Sun is about $10^{77}$ times greater than that of the Sun itself. If our star collapsed into a hole, its "information capacity" would grow enormously — as if a planet-sized library turned into a point.
In Greg Bear's novel "The Light of Distant Stars," civilizations use black hole shadows as giant gravitational lenses for intergalactic communication, but they do not realize that the shadow's shape reveals fundamental corrections to the laws of thermodynamics.