In a two-dimensional universe, a black hole looks like a funnel in spacetime. But the authors of the new work went further: they proposed that the space where particle momenta 'live' is also curved, like a saddle. They took an ordinary BTZ black hole (a three-dimensional relative of real black holes) and added quantum ripples to the geometry of momenta.

This curvature changes the rules of the game for particles near the black hole. The mass of the hole itself gets a small quantum addition, as if an invisible sculptor slightly adjusts its shape. The event horizon (the boundary from which nothing can escape) shifts a bit. And the temperature and entropy of the hole (a measure of its hidden information) acquire Planck-scale corrections. What is surprising is that Einstein's equations of gravity remain untouched. The effect comes not from quantizing spacetime but from the quantum nature of motion itself.

The authors tested the model on Hawking radiation black_hole]. Using the tunneling method (a particle effectively leaks through the horizon), they found that the return time of an emitted massless particle gets two contributions. One comes from the curvature of momentum space, the other from the backreaction of radiation on the hole. But the particle trajectories, their null geodesics, do not change. So all the oddities stem from the deformation of the effective geometry, not from new forces. The quantum dance of momenta gives rise to gravitational phenomena without touching the fabric of spacetime itself.