Action growth for AdS black holes
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Publication:1636238
DOI10.1007/JHEP09(2016)161zbMATH Open1390.83180arXiv1606.08307OpenAlexW2600101568MaRDI QIDQ1636238
Author name not available (Why is that?)
Publication date: 12 June 2018
Published in: (Search for Journal in Brave)
Abstract: Recently a Complexity-Action (CA) duality conjecture has been proposed, which relates the quantum complexity of a holographic boundary state to the action of a Wheeler-DeWitt (WDW) patch in the anti-de Sitter (AdS) bulk. In this paper we further investigate the duality conjecture for stationary AdS black holes and derive some exact results for the growth rate of action within the Wheeler-DeWitt (WDW) patch at late time approximation, which is supposed to be dual to the growth rate of quantum complexity of holographic state. Based on the results from the general -dimensional Reissner-Nordstr"{o}m (RN)-AdS black hole, rotating/charged Ba~{n}ados-Teitelboim-Zanelli (BTZ) black hole, Kerr-AdS black hole and charged Gauss-Bonnet-AdS black hole, we present a universal formula for the action growth expressed in terms of some thermodynamical quantities associated with the outer and inner horizons of the AdS black holes. And we leave the conjecture unchanged that the stationary AdS black hole in Einstein gravity is the fastest computer in nature.
Full work available at URL: https://arxiv.org/abs/1606.08307
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