Abstract
We calculate the holographic entanglement entropy for the rotating cylindrical black holes in d+1 dimensions as perturbations over AdSd+1. This is accomplished based on the first order variation of the area functional in arbitrary dimensions. For these types of black holes, the angular momentum appears at the first order of the perturbative expansion of the holographic entanglement entropy for spacetime dimensions of d + 1 ≥ 4. We obtain a form of holographic entanglement first law in the presence of both energy and angular momentum.
Highlights
Entanglement entropy (EE), as a common quantity in quantum field theory (QFT), is investigated in various field including that of quantum information
Ryu and Takayanagi (RT) proposed a relationship to hold between the EE of the subsystem A on the d dimensional conformal field theory (CFT) side and the area of d − 1 dimensional minimal surfaces anchored at the boundary of AdSd+1 on the entangling surface [4, 5]
If we use the method of Ref. [8] to obtain δ S1 for the metric (21), we find the same expression (28) for the holographic entanglement entropy (HEE) of the planar AdS black holes
Summary
Entanglement entropy (EE), as a common quantity in quantum field theory (QFT), is investigated in various field including that of quantum information. Various perturbative methods may be used to evaluate the HEE in the presence of desired non-rotating black holes in the bulk [7,8,9,10]. In this situation, the following relation may be derived for ∆SA:. The entanglement temperature and the entanglement angular velocities are obtained as functions of the rotation parameters of rotating cylindrical black holes
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