QFT
In the literature: partially resolved
Derive full nonlinear Einstein equations from boundary entanglement
In plain words
Small ripples of spacetime obeying Einstein's equations have been derived from rules about entanglement. The same for strongly curved spacetime has not been done.
Precise statement
The entanglement first law plus the Ryu-Takayanagi formula implies the linearized Einstein equations around AdS (Faulkner, Guica, Hartman, Myers, Van Raamsdonk 2014), extended to second order in 2017. Derive the full nonlinear bulk Einstein equations with matter from CFT entanglement constraints, or identify the additional input required.
What would settle it
A derivation of the nonlinear Einstein equations from boundary entropy relations, or a demonstration that extra CFT input is needed.
Status in the literature
Linear order derived in 2014 and second order in 2017; the nonlinear case is open.