Holographic complexity of the extended Schwarzschild-de Sitter space

• DOI: 10.1007/jhep05(2024)201
• Publication Date: 2024-05-21T15:04:16Z
• Authors: Sergio E. Aguilar...; Stefano Baiguera; Nicolò Zenoni
• Keywords: High Energy Physics - Theory; AdS-CFT Correspondence; de Sitter space; Models of Quantum Gravity;; de Sitter space; FOS: Physical sciences; QC770-798; General Relativity and Quantum Cosmology (gr-qc); AdS-CFT Correspondence; 01 natural sciences; General Relativity and Quantum Cosmology; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Models of Quantum Gravity

Abstract

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.