Holographic complexity of the extended Schwarzschild-de Sitter space

• Published in: The journal of high energy physics Vol. 2024; no. 5; pp. 201 - 67
• Main Authors: Aguilar-Gutierrez, Sergio E., Baiguera, Stefano, Zenoni, Nicolò
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 16.05.2024; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black holes; Classical and Quantum Gravitation; Complexity; de Sitter space; Elementary Particles; Entropy; Geometry; Holography; Models of Quantum Gravity; Physics; Physics and Astronomy; Proposals; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spacetime; String Theory; AdS-CFT Correspondence; Models of Quantum Gravity; de Sitter space
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2024)201

A bstract According to static patch holography, de Sitter space admits a unitary quantum description in terms of a dual theory living on the stretched horizon, that is a timelike surface close to the cosmological horizon. In this manuscript, we compute several holographic complexity conjectures in a periodic extension of the Schwarzschild-de Sitter black hole. We consider multiple configurations of the stretched horizons to which geometric objects are anchored. The holographic complexity proposals admit a hyperfast growth when the gravitational observables only lie in the cosmological patch, except for a class of complexity=anything observables that admit a linear growth. All the complexity conjectures present a linear increase when restricted to the black hole patch, similar to the AdS case. When both the black hole and the cosmological regions are probed, codimension-zero proposals are time-independent, while codimension-one proposals can have non-trivial evolution with linear increase at late times. As a byproduct of our analysis, we find that codimension-one spacelike surfaces are highly constrained in Schwarzschild-de Sitter space. Therefore, different locations of the stretched horizon give rise to different behaviours of the complexity conjectures.