Holographic complexity of de Sitter black holes
Abstract
We investigate holographic complexity within the Schwarzschild-de Sitter (SdS) black hole spacetime. Two distinct de Sitter holography prescriptions are examined: the static patch scheme restricted to the stretched horizon and the de Sitter/Conformal Field Theory (dS/CFT) correspondence scheme defined at asymptotic future and past infinities. We evaluate the Complexity equals Volume (CV) conjecture and extend the analysis to codimension-zero proposals, specifically Complexity equals Spacetime Volume (CV2.0) and Complexity equals Action (CA), through the Wheeler-DeWitt (WDW) patch we construct. The behaviors of the complexity in the static patch holography at late time and in the dS/CFT at infinite spacelike boundary coordinate are studied, respectively. We find that under both the CV and CV2.0 conjectures, the static patch holographic complexity and the dS/CFT holographic complexity consistently exhibit linear growth. Conversely, regarding the CA conjecture, the holographic complexity growth rates for both the static patch and the dS/CFT correspondence vanish. This behavior is attributed to the finiteness of the (regularized) action within the restricted WDW region. Furthermore, we find that, in the limit in which the boundary coordinate is taken to infinity, the complexity growth rate in the static patch prescription coincides with its counterpart in the dS/CFT prescription. This agreement suggests a deeper connection between the two descriptions and may point toward a unified understanding of bulk dynamics in de Sitter holography.
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BibTeX
@misc{fang2026holographic,
title = {{Holographic complexity of de Sitter black holes}},
author = {Chaoxi Fang and Jiayue Yang and Shao-Wen Wei and Ming Zhang and Robert B. Mann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.03049},
eprint = {2606.03049},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03049},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Holographic complexity of de Sitter black holes
AU - Chaoxi Fang
AU - Jiayue Yang
AU - Shao-Wen Wei
AU - Ming Zhang
AU - Robert B. Mann
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2606.03049
UR - https://arxiv.org/abs/2606.03049
AB - We investigate holographic complexity within the Schwarzschild-de Sitter (SdS) black hole spacetime. Two distinct de Sitter holography prescriptions are examined: the static patch scheme restricted to the stretched horizon and the de Sitter/Conformal Field Theory (dS/CFT) correspondence scheme defined at asymptotic future and past infinities. We evaluate the Complexity equals Volume (CV) conjecture and extend the analysis to codimension-zero proposals, specifically Complexity equals Spacetime Volume (CV2.0) and Complexity equals Action (CA), through the Wheeler-DeWitt (WDW) patch we construct. The behaviors of the complexity in the static patch holography at late time and in the dS/CFT at infinite spacelike boundary coordinate are studied, respectively. We find that under both the CV and CV2.0 conjectures, the static patch holographic complexity and the dS/CFT holographic complexity consistently exhibit linear growth. Conversely, regarding the CA conjecture, the holographic complexity growth rates for both the static patch and the dS/CFT correspondence vanish. This behavior is attributed to the finiteness of the (regularized) action within the restricted WDW region. Furthermore, we find that, in the limit in which the boundary coordinate is taken to infinity, the complexity growth rate in the static patch prescription coincides with its counterpart in the dS/CFT prescription. This agreement suggests a deeper connection between the two descriptions and may point toward a unified understanding of bulk dynamics in de Sitter holography.
ER -