Noether charge, black hole volume, and complexity
By Josiah D. Couch, W. Fischler, P. Nguyen. 2016
244 citations recorded by the source corpus.
A bstractIn this paper, we study the physical significance of the thermodynamic volumes of AdS black holes using the Noether charge formalism of Iyer and Wald. After applying this formalism to study the extended thermodynamics of a few examples, we discuss how the extended thermodynamics interacts with the recent complexity = action proposal of Brown et al. (CA-duality). We, in particular, discover that their proposal for the late time rate of change of complexity has a nice decomposition in terms of thermodynamic quantities reminiscent of the Smarr relation. This decomposition strongly suggests a geometric, and via CA-duality holographic, interpretation for the thermodynamic volume of an AdS black hole. We go on to discuss the role of thermodynamics in complexity = action for a number of black hole solutions, and then point out the possibility of an alternate proposal, which we dub “complexity = volume 2.0”. In this alternate proposal the complexity would be thought of as the spacetime volume of the Wheeler-DeWitt patch. Finally, we provide evidence that, in certain cases, our proposal for complexity is consistent with the Lloyd bound whereas CA-duality is not.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b4ad23801dc762177676b2b12c28d9c983af3079
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Citations in the corpus
- Holographic complexity in Vaidya spacetimes. Part I (2018, background): “Some initial studies of this question appear in [95, 96], which examine the evolution of the complexity through a mass quench in a (30)Violations of the analogous bound proposed for systems with a chemical potential were also found in certain instances [30, 93, 94].”
- Comments on holographic complexity (2016, background): “An alternative proposal related to complexity=volume was recently put forward in [11].”
- Complexity of formation in holography (2016, background): “An alternative proposal related to complexity=volume was recently put forward by [43].”
- Holographic complexity in Vaidya spacetimes. Part II (2018, background): “5,96], which examine the evolution of the complexity through a mass quench in a 30Violations of the analogous bound proposed for systems with a chemical potential were also found in certain instances [30,93,94]. { 46 { free scalar eld theory (analogous to those studied in [82{84]). A remarkable feat”