Collapsing stars and planets cannot spin infinitely fast as they crash into each other, resolving a paradox that has puzzled mathematicians for decades.
April 29, 2026
Original Paper
No infinite spin for total collisions in the spatial N-body problem
arXiv · 2604.22172
The Takeaway
Celestial mechanics equations theoretically allowed for a singularity where objects rotate at infinite speeds as they collapse into a single point. This new proof shows that such a scenario is physically impossible under standard conditions. The geometric shape of the group prevents the rotational energy from spiraling out of control. It sets a hard limit on how energy behaves during the most violent gravitational events in space. This provides a more stable foundation for simulating how star clusters and solar systems end their lives.
From the abstract
In the $n$-body problem, when bodies tend to a total collision, then its normalized shape curve converges to the set of normalized central configurations, which has $SO(3)$ symmetry in the planar case. This leaves a possibility that the normalized shape curve tends to the set obtained by rotations of some central configuration instead of a particular point on it. This is the \emph{infinite spin problem} which concerns the rotational behavior of total collision orbits in the $n$-body problem. We