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Drop a pebble into a pond, and ripples spread across the water. A black hole 'sounds' much the same when matter falls into it or when its spacetime gets a gentle jolt. These fading oscillations are called quasinormal modes, like the tolling of a bell that gradually fades away.

The authors of the study didn't take an ordinary black hole but one corrected for loop quantum gravity, an approach where space itself is made of tiny 'loops.' They placed such a hole in a world with extra dimensions (as if our three-dimensional world were just a film in a higher-dimensional space) and added a weak repulsion — the cosmological constant (the thing that makes the universe expand faster and faster). Then they calculated how this hole would oscillate under light scalar perturbations — the simplest kind of waves, like sound waves but for space itself.

It turned out that quantum corrections only slightly shift the frequencies, but changing the number of dimensions alters the picture dramatically: oscillations become more frequent and damp out faster. All modes proved stable — the hole doesn't get destroyed by such perturbations. The researchers then constructed the black hole's shadow — the dark silhouette against a bright ring that arises from the bending of light rays. The shadow size is sensitive to the quantum parameter, the cosmological constant, and especially to the number of dimensions: the more dimensions, the smaller the shadow.

By comparing the theoretical shadow radius with observational data for the M87 hole, the authors obtained constraints on the model's parameters. This means that future observations of gravitational waves and black hole shadows could become two independent ways to test whether space has extra dimensions and whether loop quantum gravity works in strong fields. The pebble has been thrown, the ripples are spreading.