Is there a holographic dual for non-extremal Kerr black holes?
In plain words
Rapidly spinning black holes show a hidden symmetry that lets their entropy be computed with a formula from two-dimensional quantum field theories. Whether such a theory really exists for ordinary spinning black holes, like those seen by gravitational-wave detectors, is unknown.
Precise statement
The Kerr/CFT correspondence reproduces $S = 2\pi J/\hbar$ for extremal Kerr via the Cardy formula with central charge $c_L = 12 J/\hbar$, and hidden conformal symmetry of low-frequency wave equations (2010) extends the Cardy match to non-extremal Kerr. Determine whether a unitary 2D CFT, or another quantum system, with these central charges exists whose states are the microstates of generic Kerr with $0 < a < M$. An answer is a construction or an obstruction (for example inconsistency of the boundary conditions or of modular invariance).
What would settle it
Construction of a consistent dual quantum system for generic Kerr, or a proof that the required boundary conditions admit no unitary dual.
Status in the literature
Unverified note
Entropy matches hold, but no dual theory has been constructed as of 2026.