Are typical black hole microstates horizonless geometries?
In plain words
The fuzzball proposal says each microscopic state of a black hole is a horizonless tangle of strings and branes, so there is no interior at all. The known smooth examples account for far fewer states than the black hole entropy requires.
Precise statement
For the D1-D5-P black hole with $S = 2 \pi \sqrt{N1 N5 N_P}$, determine whether typical microstates are described by horizonless smooth or stringy geometries that differ from the black hole at the horizon scale. Known supergravity families (superstrata) have entropy growing parametrically slower than $S$. An answer is a count showing whether horizonless solutions, including string-scale ones, saturate $S$, or a proof that typical states are indistinguishable from the black hole outside a Planck-scale or string-scale neighborhood of the horizon.
What would settle it
A microstate count in string theory resolving how many D1-D5-P states have horizon-scale geometric structure.
Status in the literature
Unverified note
Counts of superstrata (2019-2020) fall parametrically short of S; whether stringy states close the gap is open as of 2026.