GRAV
In the literature: open
Does every generic gravitational collapse settle to Kerr black holes?
In plain words
The final state conjecture says that any isolated system eventually becomes a set of Kerr black holes moving apart plus outgoing gravitational radiation. Stability of a single Kerr black hole covers only the small-disturbance part of this claim.
Precise statement
For generic asymptotically flat vacuum (or reasonable matter) initial data in 3+1 dimensions, prove that the maximal development is asymptotically a finite collection of boosted Kerr black holes plus radiation, possibly with a dispersing part. An answer is a proof or a counterexample.
What would settle it
A global theorem on the late-time structure of generic large-data vacuum spacetimes.