A magnetic field can hold a star against complete collapse: that's the idea behind a new kind of black hole. Instead of the usual point of infinite density, inside there is a field that prevents space from crunching down to zero. It's like a spring: the harder you squeeze, the more it pushes back.
The authors took an existing spacetime geometry and matched it with matter — a magnetic field tied to a scalar field (which sets the strength at each point). The key parameter here is the magnetic charge, like the number of field lines threading the hole. If the charge is small, the event horizon (the boundary from which light cannot escape) disappears, leaving a naked singularity, but such cases are ruled out. Using the shadow image of the black hole at the center of the Milky Way, taken by the Event Horizon Telescope, they were able to constrain the charge: it cannot be too large, otherwise the shadow would be noticeably smaller.
In thermodynamics, such a hole behaves familiarly: it has temperature and entropy, obeys the first law (energy conservation), and the Smarr formula (relating mass, horizon area, and charge). Upon heating, it can transition from empty space into a black hole: this is the Hawking–Page phase transition, like ice melting. But unlike water, there is no critical point with vigorous boiling — stability changes smoothly. Topological analysis confirms: in its global properties, this hole is a relative of the charged Reissner–Nordström hole, just without electric charge.
If the black hole at the center of the Galaxy had a noticeable magnetic charge, its shadow in the image would be a third smaller, and that would have been spotted immediately.
In Greg Egan's novel "The Light of Other Stars," magnetic monopoles are used to stabilize wormholes — here a similar idea supports the black hole itself.