Abstract
In this paper, we investigate the entanglement entropy of the rotating BTZ black hole perturbed by a massive back-reacting free falling particle. Then, mutual information between two finite intervals in two asymptotic regions of rotating BTZ is derived. It allows us to find the scrambling time, the time scale in which mutual information vanishes. We give a dual large c CFT description in terms of a thermofield double state with different temperatures for left and right moving modes that is perturbed by a local operator. Exact matching between gravity and CFT results is obtained.
Highlights
In this paper, we investigate the entanglement entropy of the rotating BTZ black hole perturbed by a massive back-reacting free falling particle
We give a dual large c CFT description in terms of a thermofield double state with different temperatures for left and right moving modes that is perturbed by a local operator
In our previous paper [14] the scrambling time was computed in two dimensional large c CFT in thermofield double (TFD) state
Summary
Consider two 2d CFTs with Hamiltonian H and momentum P on Hilbert spaces HL and HR. We can construct an entangled thermofield double state on HL ⊗ HR [19,20,21,22,23]. Mutual information in the perturbed TFD state was discussed in [20, 21, 24]. We will generalize the formalism developed in [14] where perturbed TFD state was dual to the non-rotating eternal BTZ black hole. As in [14] we consider TFD state excited with a primary operator ψ(0, −tω) in the CFTL at time −tω in the past. In order to calculate density matrix, we will have two copies of ψ inserted at the same point. This can be avoided by spreading out perturbation on a scale which we choose to be much larger than ultraviolet cut-off UV.
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