Does interior volume growth equal computational complexity of the dual state?
In plain words
The volume inside an eternal black hole keeps growing for an extremely long time, long after the outside has settled down. One proposal ties this growth to the growing complexity of the quantum state that describes the black hole.
Precise statement
For the two-sided AdS-Schwarzschild black hole, the maximal-volume slice anchored at boundary time t grows as $V(t)\ \text{proportional to}\ t$ up to times of order $\operatorname{exp}(S)$. Determine whether a precisely defined boundary quantity (circuit complexity, Krylov complexity, or another) of the thermofield-double state equals $V/(G \ell_{\mathrm{AdS}})$ up to normalization, including saturation at $t \sim \operatorname{exp}(S)$ and the switchback response to perturbations. An answer is a boundary definition with proven matching properties or a demonstration that no unique quantity is singled out.
What would settle it
A boundary-defined quantity shown to reproduce the growth, saturation and perturbation response of the interior volume, unique up to stated equivalences.
Status in the literature
Unverified note
Many inequivalent bulk quantities share the same growth and switchback features (complexity equals anything, 2021-2022), so the boundary dual is not fixed as of 2026.