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In classical theory, a black hole is where matter collapses to a point of infinite density. Such a 'singularity' looks like an error in the equations: nature hardly tolerates infinities. Many physicists seek ways to 'smooth out' this flaw, and one idea is to modify the theory of gravity itself at small distances.

The authors of the new work build on so-called quasi-topological gravities — extensions of Einstein's theory that add more complex combinations of spacetime curvature to the equations. Usually, such theories suffer from 'ghosts' (particles with negative energy) or strong coupling (where small perturbations trigger uncontrollable responses). Here, they propose an 'infinite-derivative' version: the gravitational interaction is 'smeared' over time, which kills ghosts and makes the theory stable.

In this theory, the authors found exact solutions for spherical black holes. Inside the event horizon, instead of a point of infinite curvature, there is a regular core — a region where curvature is finite. This is like a sink drain with a rounded bottom: water flows out, but without tearing the fabric of space. Moreover, for these solutions, Birkhoff's theorem holds — the gravitational field outside a spherical object does not depend on what happens inside; it is determined solely by the total mass.

This work is not the final answer but rather a demonstration that one can build a consistent theory with regular black holes without introducing exotic matter. It opens a path to exploring quantum corrections to gravity without paradoxes. If astronomers ever manage to peer beneath the event horizon, such models will hint at what they might see.