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Phase portrait of near-extremal dynamics (Conjecture)

Characterize the moduli space of characteristic initial data near extremal Kerr by proving that the codimension-1 stability hypersurface separates data evolving to subextremal black holes from data not collapsing in the domain of dependence (yielding incomplete null infinity without horizon formation), thereby furnishing the phase portrait of near-extremal vacuum Einstein dynamics.

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Background

The conjecture complements the codimension-1 stability claim by describing how initial data near extremal Kerr partition into regions that evolve to subextremal black holes or to noncollapse spacetimes with incomplete null infinity, with the stability hypersurface providing the boundary.

This phase space structure has implications for interpreting overspinning/overcharging scenarios and for understanding threshold behavior such as extremal critical collapse.

References

Conjecture Under the assumptions of Conjecture 1, the codimension-1 “submanifold” M_stable is in fact a regular hypersurface which separates the moduli space M into two open regions, each with boundary M_stable: the set of initial data M_subextremal evolving to subextremal black holes and the set of initial data M_noncollapse not collapsing in the domain of dependence of the data, i.e. such that the domain of dependence of the data is entirely contained in J-(I+) (but with incomplete I+).

— Black Holes Inside and Out 2024: visions for the future of black hole physics (2410.14414 - Afshordi et al., 18 Oct 2024) in Mihalis Dafermos, Section "The stability conjecture for extremal black holes and the phase portrait of near extremal dynamics" (Conjecture 2)