Usually, a black hole is described as a frozen frame: there's mass, there's charge, and it's all static. But real objects live in time. They radiate, lose energy, and change.
The authors of the new work took a static solution for a charged black hole in a complex theory of gravity and "brought it to life." They allowed mass and charge to depend on time — somewhat like the temperature of a kettle depends on how long ago it was turned off. To keep the equations from falling apart, they had to add flows that carry away energy and charge, like steam rising from hot water.
This approach is not just a mathematical toy. It provides a simple recipe for constructing exact solutions where a black hole or another compact object actually radiates. In the future, this could help model how black holes behave in binary systems or during mergers, when energy and charge flows become important.
The idea of a "living" solution where mass and charge depend on time recalls the old Vaidya model from 1951. Back then, it was devised for ordinary gravity, and now it has been generalized to more complex theories that attempt to explain dark matter and the expansion of the universe.
In Stanisław Lem's novel "Solaris," the ocean alters the metric of spacetime as if it were a living being. Here, the metric also ceases to be frozen — though according to strict physical laws, not by the will of a mind.