Scrambling time for analogue black holes embedded in AdS space

Abstract

We propose a gedanken experiment on realizing thermofield double state (TFD) by using analog black holes and provide an approach to test the scrambling time. Through this approach, we demonstrate clearly how shock wave changes the TFD state as time evolves. As the whole system evolves forward in time, the perturbation of spacetime geometry will increase exponentially. Finally, it will destroy the entanglement between the two states of the thermal field, and the mutual information between them is reduced to zero in the time scale of scrambling. The results show that for perturbations of analogue black holes embedded in AdS space, the scale of the scrambling time is closely related to the logarithm of entropy of the black hole. The results provide further theoretical argument for the scrambling time, which can be further falsified in experiments.

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“…In the last line, we assume that b has the order O(r + ) and the acceleration is not large (α ≪ 1 r + ). This result follows the conclusion of the initial Hayden-Preskill experiment [87,88]. Then, the scrambling time as a function of the acceleration α and the charge Q is plotted in Figure .6.…”

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