A regular black hole model with a smooth core instead of a singularity, violating energy conditions.A Bardeen black hole is a theoretical model of a black hole that avoids the central singularity—a point of infinite density—by having a smooth, regular core. Instead of collapsing to a point, the matter is spread out over a small region, and the spacetime curvature remains finite everywhere. This model was proposed to address the breakdown of physics at singularities, suggesting that quantum gravity effects might prevent their formation.
The model was introduced by James Bardeen in 1968, who proposed it as a regular black hole solution, though it was initially considered a mathematical curiosity.
In general relativity, a black hole's singularity is hidden behind an event horizon. The Bardeen model modifies the metric (the mathematical description of spacetime) by introducing a magnetic charge or a similar parameter that acts as a cutoff, smoothing the gravitational field at very small distances. This solution satisfies the Einstein equations but requires the energy-momentum tensor to violate certain energy conditions, meaning the matter has exotic properties like negative pressure.
Bardeen black holes are used in theoretical studies of quantum gravity and as testbeds for understanding the information paradox and the nature of spacetime singularities.
The Bardeen black hole is often called a 'regular black hole' because it has no singularity, but it still possesses an event horizon, making it a black hole in the traditional sense.

