[lowpro]

General question: where does this research lead to? As in what might be the next step for this research team, and/or their field in general? I always like to understand what discoveries like this could open up in the future.

*Asking as someone not in the field or any type of physics/mathematics

[jstogin]

There are theoretical and potentially practical implications for this work. Black hole stability can be considered a kind of stress-test for General Relativity as a theory. If we believe the universe has rotating black holes, then we expect a valid theory to predict they are stable (or at least not catastrophically unstable). So a stability result helps validate the theory by at least showing there's one fewer way to refute it.

Some parts of the proof may actually be more insightful or practical than the result itself, but they don't get discovered or understood in detail until someone sits down and attempts to prove the result. If I had to guess, the most likely truly practical implication might be that some of the insights within the proof could help with numerical simulations of black holes. And if they help with numerical simulations of black holes, they might also help with numerical simulations of other PDEs that are more relevant in engineering.

[curt15]

I don't know if there's any rigorous mathematical work yet on multiple black-hole space times.