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3 November 2025

Science China Press/Guo, et alA sequence of snapshots simulating the rotating Hayward black hole

A few days ago, I wrote about non-singular black hole models, specifically one known as the Hayward model. Since its introduction in 2006, several variations of the Hayward model have been introduced, including a rotating model similar to the Kerr metric used to study the supermassive black holes we’ve observed directly. This raises an interesting question: what if we use a rotating Hayward model instead of the usual Kerr model? A recent study answers that question.1

From the outside, Hayward black hole metrics are nearly the same as the usual Schwarzschild black hole metrics. Both are solutions to Einstein’s field equations. The only difference is that Hayward solutions impose an additional constraint that the black hole have no singularity, which gets rid of a few problems around singularities and event horizons. For the exterior regions we can observe, the two models are so similar that you would think using one model over another would be pointless. But this latest work shows that the Hayward model could have some advantages.

In this latest work, the team started with a rotating Hayward metric and introduced a statistical simulation of a somewhat random plasma field. It’s similar to the way animators in movies and video games use a simulated fluttering to simulate water waves rather than computing the actual fluid dynamics of water. The result looks similar to reality but is much easier to compute. For their model, the team simulated the flickering of light emitted by the accretion disk near the black hole.

For standard black hole models, this approach mostly washes out. The random flickerings just get blurred together at the level we can observe, so it isn’t very useful for studying the dynamics of supermassive black holes. But the authors found the same isn’t true for Hayward models. Without a singularity, Hayward models have a small dynamic character to them, and the random flickerings interact with that.

For example, one of the things we’ve observed with the supermassive black hole M87* is that the magnetic field of its accretion disk can shift rather suddenly. We still aren’t entirely sure how this happens, and the computer simulations using a standard metric are very sensitive to initial conditions. But this shift of the magnetic field arises naturally in the Hayward model. In other words, this new approach gives a better simulation of what we observe.

It should be stressed that this new approach doesn’t get to the underlying physics that creates these magnetic field shifts. But that’s not necessarily a problem. Just as we can model things like friction without modeling the atomic interactions of two surfaces, this new approach could help us understand the overall dynamics of black holes.

So it turns out that non-singular black hole models have a point after all.

Guo, Sen, et al. “Image of a time-dependent rotating regular black hole.” Science China Physics, Mechanics & Astronomy 68.10 (2025): 1-16. ↩︎