Abstract
The Complexity=Action conjecture is studied for black holes in Warped AdS3 space, realized as solutions of Einstein gravity plus matter. The time dependence of the action of the Wheeler-DeWitt patch is investigated, both for the non-rotating and the rotating case. The asymptotic growth rate is found to be equal to the Hawking temperature times the Bekenstein-Hawking entropy; this is in agreement with a previous calculation done using the Complexity=Volume conjecture.
Highlights
The thermalization time, and so entropy does not provide us with a good dual quantity for this process
The Complexity=Action conjecture is studied for black holes in Warped AdS3 space, realized as solutions of Einstein gravity plus matter
A proper definition of complexity in quantum field theory has several subtleties, including the choice of the reference state and of the allowed set of elementary quantum gates and the allowed amount of tolerance which is introduced in order to specify the accuracy with which the state should be produced
Summary
We consider the following class of BHs with Warped AdS3 asymptotic [40, 51, 52]: ds l2. Where Ψ(ρ0) = 0 and we take the range of variables as follows: r0 ≤ r < ∞, −∞ < t < ∞, θ ∼ θ + 2π and the horizons are located at r = r+, r− with r+ ≥ r− These metrics can be obtained by discrete quotients of WAdS3 [40]; we take ν ≥ 1 in order to avoid closed timelike curves. We will be interested to WAdS3 BHs realized as solution of Einstein gravity with matter. All the known realizations of WAdS3 BHs in Einstein gravity have some pathology in the matter content: for example, they can be realized as solutions with perfect fluid stress tensor with spacelike quadrivelocity [61]. In order to have solutions without closed time-like curves, a wrong sign for the kinetic Maxwell term is needed. The conserved charges (mass and angular momentum) are [49, 50, 62]:
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