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تسجيل مستخدم جديدComplexity and action for warped AdS black holes
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The Complexity=Action conjecture is studied for black holes in Warped AdS$_3$ 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.
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We study the Complexity=Volume conjecture for Warped AdS$_3$ black holes. We compute the spatial volume of the Einstein-Rosen bridge and we find that its growth rate is proportional to the Hawking temperature times the Bekenstein-Hawking entropy. Thi
s is consistent with expectations about computational complexity in the boundary theory.
We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS$_3$ black holes, both for the action and the volume conjectures. Besides the linear divergences, w
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Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -ell^{-2} and positive Newton constant G admits an AdS_3 vacuum solution for any value of the graviton mass mu. These are all known to be perturbatively unsta
ble except at the recently explored chiral point muell=1. However we show herein that for every value of muell< 3 there are two other (potentially stable) vacuum solutions given by SL(2,R)x U(1)-invariant warped AdS_3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at muell=3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For muell>3, there are known warped black hole solutions which are asymptotic to warped AdS_3. We show that these black holes are discrete quotients of warped AdS_3 just as BTZ black holes are discrete quotients of ordinary AdS_3. Moreover new solutions of this type, relevant to any theory with warped AdS_3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for muell>3, the warped AdS_3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c_R={15(muell)^2+81over Gmu((muell)^2+27)} and c_L={12 muell^2over G((muell)^2+27)}.
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