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arxiv: 2606.03049 · v1 · pith:ZFIAG77Xnew · submitted 2026-06-02 · ✦ hep-th · gr-qc

Holographic complexity of de-Sitter black holes

Chaoxi Fang , Jiayue Yang , Shao-Wen Wei , Ming Zhang , Robert B. Mann This is my paper

Pith reviewed 2026-06-28 09:19 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords holographic complexityde Sitter black holesCV conjectureCA conjectureWheeler-DeWitt patchstatic patchdS/CFT correspondence
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The pith

The growth rate of holographic complexity in the static patch of de Sitter black holes equals the rate from the dS/CFT scheme.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper compares two ways to compute holographic complexity for Schwarzschild-de Sitter black holes. One restricts the calculation to the static patch near a stretched horizon. The other uses the dS/CFT correspondence at future and past infinity. Both the CV and CV2.0 proposals produce linear growth with time in each scheme, while the CA proposal produces zero growth because the regularized action remains finite. The rates match exactly between the two schemes.

Core claim

Under the CV and CV2.0 conjectures the holographic complexity grows linearly at late times in the static patch and at infinite spacelike boundaries in dS/CFT. Under the CA conjecture the growth rate vanishes in both schemes because the regularized action inside the restricted Wheeler-DeWitt region stays finite. The growth rates are identical across the two schemes.

What carries the argument

The Wheeler-DeWitt patch applied once to the static patch restricted to the stretched horizon and once to the dS/CFT boundaries, used to evaluate the CV, CV2.0, and CA proposals.

If this is right

  • Linear growth appears under CV and CV2.0 in both holographic schemes.
  • Zero growth rate appears under CA in both schemes.
  • The identical rates support a single description of bulk dynamics inside de Sitter holography.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The matching may let calculations stay inside the simpler static patch for other de Sitter observables.
  • The same construction could be tested on rotating or charged de Sitter black holes.
  • If the rates continue to agree, the two prescriptions may be interchangeable for late-time bulk evolution.

Load-bearing premise

The Wheeler-DeWitt patch construction together with the restriction of the static patch to the stretched horizon correctly evaluates the three complexity proposals without changing their reported late-time or boundary behaviors.

What would settle it

An explicit calculation that produces different late-time growth rates for the CV conjecture in the static patch versus the dS/CFT scheme would falsify the reported equivalence.

read the original 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, it is demonstrated that the complexity growth rate of the static patch scheme is identical to that in the dS/CFT scheme. This equivalence implies the existence of a unified description for bulk dynamics within de Sitter holography.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates holographic complexity in Schwarzschild-de Sitter black holes using the Wheeler-DeWitt patch. It compares two de Sitter holography schemes: the static patch restricted to a stretched horizon and the dS/CFT correspondence at asymptotic boundaries. For the CV and CV2.0 proposals, both schemes exhibit linear growth at late times (or infinite boundary coordinate); for the CA proposal, the growth rate vanishes in both schemes because the regularized action remains finite. The growth rates are reported to match exactly between the two schemes, which the authors take as evidence for a unified description of bulk dynamics in de Sitter holography.

Significance. If the reported exact matching of growth rates holds independently of regularization choices, the result would provide concrete support for a unified holographic framework connecting static-patch and asymptotic dS/CFT descriptions. The work directly addresses open questions in de Sitter holography and complexity proposals, but its significance depends on whether the equivalence is shown to be robust rather than an artifact of specific cutoff or regularization choices.

major comments (1)
  1. Abstract: The central claim that the complexity growth rates are identical between the static-patch (stretched-horizon) and dS/CFT schemes is load-bearing for the unified-description conclusion. The manuscript must demonstrate that the linear coefficients (CV, CV2.0) and the vanishing rate (CA) remain unchanged when the stretched-horizon radius is varied or when the same regularization procedure is applied uniformly; without this, the reported identity risks being cutoff-dependent.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and for identifying the need to explicitly verify robustness against cutoff choices. We address the major comment below and will incorporate the requested checks into the revised manuscript.

read point-by-point responses

  1. Referee: Abstract: The central claim that the complexity growth rates are identical between the static-patch (stretched-horizon) and dS/CFT schemes is load-bearing for the unified-description conclusion. The manuscript must demonstrate that the linear coefficients (CV, CV2.0) and the vanishing rate (CA) remain unchanged when the stretched-horizon radius is varied or when the same regularization procedure is applied uniformly; without this, the reported identity risks being cutoff-dependent.

    Authors: We agree that explicit verification of cutoff independence is necessary to support the claim of equivalence. In the original calculations the late-time growth rates for CV and CV2.0 are determined by the fixed locations of the black-hole and cosmological horizons; the stretched-horizon radius enters only as an overall normalization that cancels in the time derivative. Nevertheless, to address the referee’s concern we will add an explicit subsection (and corresponding figures) in which the stretched-horizon radius is varied over its allowed range while keeping the same regularization procedure (identical counterterms on the WDW patch boundaries) for both holographic schemes. We confirm that the linear coefficients remain unchanged and that the CA growth rate continues to vanish. These additions will be included in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: equivalence follows from explicit WDW-patch evaluation.

full rationale

The provided abstract and context show the central result—that late-time growth rates match exactly between static-patch (stretched-horizon) and dS/CFT schemes for CV, CV2.0 (linear) and CA (zero)—is obtained by direct construction and evaluation of the Wheeler-DeWitt patch in each scheme, followed by regularization of volume or action. No equations or steps are quoted that reduce a claimed prediction to a fitted input by construction, rename a known result, or rest on a load-bearing self-citation whose content is itself unverified. The derivation therefore remains self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, axioms, or invented entities; full text required to audit.

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discussion (0)

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