Abstract
We provide a formula to reconstruct bulk spacetime metrics inside black holes by the time dependence of complexity in the dual quantum field theory, based on the complexity=volume (CV) conjecture in the holographic duality.
Highlights
Interior, because the dual thermal QFT data is associated with the asymptotic boundary of the bulk spacetime, and the bulk classical gravity does not extract information inside the static horizon
We provide a formula to reconstruct bulk spacetime metrics inside black holes by the time dependence of complexity in the dual quantum field theory, based on the complexity=volume (CV) conjecture in the holographic duality
The CV conjecture [59, 60] states that the quantum computational complexity of a thermo-field double state at a time in the dual QFT is equal to the volume of an extremal surface in the bulk penetrating the horizon and anchored to the boundary at the QFT time
Summary
We provide the formula to reconstruct the interior of a black hole by the complexity in the dual QFT, based on the complexity=volume (CV) conjecture [55, 59]. V (t) is the volume of the extremal surface defined in the two-sided eternal AdS black holes. The surface is anchored at time t at the two boundaries of the spacetime. GN is the Newton’s constant and L is the AdS radius
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