object

bardeen black hole

A regular black hole model with a smooth core instead of a singularity, violating energy conditions.
13 related articles

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

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Related articles · 13

General Relativity2026-08-052 minarXiv:2608.04461express
The Black Hole Trampoline: A Jump Through the Horizon
The idea was elegant: take a BTZ black hole (the three-dimensional analog of a regular black hole) and smooth its horizon with a special function. The hope was that inside, the spacetime signature might change — time becoming space, and space becoming time. But the calculations showed otherwise.
General Relativity2026-08-032 minarXiv:2608.02481express
The Heart of a Black Hole: Why a Smooth Center Isn't Everything
An old house. The facade is freshly painted, the stairs don't creak. A pretty picture. But try to move in heavy furniture, and the floorboards give way. The beauty of the facade says nothing about the strength of the floors. It's much the same with black holes without singularities.
General Relativity2026-07-211 minarXiv:2607.18764express
A Black Hole with No Bottom: Why Gravastars Can't Hold Up
A campfire burns steadily and long. But when the wind blows, the flame flickers out, leaving only embers. A similar story plays out with the gravastar — a hypothetical object that was supposed to replace the black hole. An ordinary black hole hides a singularity — a point where the laws of physics break down.
General Relativity2026-06-212 minarXiv:2606.22404express
A Black Hole Turns White: What Has to Break
Light passing near a massive body slightly changes its path — gravity pulls even on rays. In ordinary situations, a beam of light from a distant star is squeezed as if drawn together by an invisible rubber band. This property is called the null convergence condition: gravity makes light trajectories converge rather than diverge.
General Relativity2026-06-122 minarXiv:2606.14537express
Dark Matter as a Quantum Droplet
At the center of many galaxies lurks an invisible halo of dark matter: it holds the stars at the edges, keeping them from flying apart. For a long time, it was described as a dilute gas of particles, but new work offers a different view: dark matter might gather into a quantum droplet.
Galaxies2026-05-271 minarXiv:2605.29069express
Dark Matter: Quantum Vortices Around Black Holes
In the quantum world, dark matter particles can merge into a single superfluid droplet — a state where matter flows without friction, like an ideal fluid. When near a black hole, this droplet doesn’t just disappear into it but twists into stable vortices, like water swirling around a rock in a stream.
General Relativity2026-05-122 minarXiv:2605.11364express
A Black Hole Rings Differently If There's No Singularity at Its Core
Drop a pebble into a well, and the sound tells you its depth. That's roughly how astrophysicists listen to black holes: after a merger or other disturbance, the hole vibrates, emitting gravitational waves. The frequency and damping of this 'ring' depend on what's inside the hole.
Cosmology2026-05-072 minarXiv:2605.05679express
Cosmic Orchestra Tests Dark Matter
Two heavy balls orbit on the surface of a pond. Ripples spread from them: these are gravitational waves. As the balls spiral closer, the waves carry away energy, and the ripples become more frequent.
HEP Theory2026-05-041 minarXiv:2605.02523express
A Black Hole with Quantum Armor
You can picture a black hole as a whirlpool in a river: it has an edge, the event horizon, beyond which the current drags everything in irreversibly. At the center lurks the singularity, a point where the familiar laws break down.
General Relativity2026-04-222 minarXiv:2604.20066express
HEP Theory2026-04-212 minarXiv:2604.19920express
Gravity and Electricity: The Double Life of Black Holes
A translator retells a complex novel in another language, but only if the plot stands still. Once the characters start moving, the translator loses the thread. That's roughly how the 'double copy' worked — a method linking gravity and electricity. Until recently, it could only handle static black holes, where time plays no role.
General Relativity2026-03-212 minarXiv:2603.20596express
What Black Holes Without Singularities Hide: From Hypotheses to Testing
Classical black holes, regions of spacetime with gravity so strong that even light cannot escape, according to general relativity, hide a singularity at their center: a point of infinite density and curvature where the known laws of physics break down.
Cosmology2026-03-131 minarXiv:2603.13137express
Dark Energy Didn’t Kick In Right Away
Dark energy is usually seen as an innate property of the cosmos, at work from the very first moments. But a new model suggests it behaved like water on the verge of boiling: long unnoticed, then suddenly kicking in at a critical moment. This scenario is called 'late activation': around 5–7 billion years ago, a shift occurred, and the universe’s expansion began to accelerate.