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arxiv: 2604.15730 · v1 · submitted 2026-04-17 · ✦ hep-th

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Stringy Effects on Holographic Complexity: The Complete Volume in Dynamical Spacetimes

Qi Yang, Yu-Xiao Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 08:43 UTC · model grok-4.3

classification ✦ hep-th
keywords holographic complexityGauss-Bonnet gravitycomplete volume proposalVaidya spacetimesshock wavesscrambling timenull shells
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The pith

Gauss-Bonnet corrections preserve the momentum-governed growth of holographic complexity in dynamical spacetimes despite velocity jumps at null shells.

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

The paper investigates stringy effects from Gauss-Bonnet gravity on holographic complexity via the complete volume proposal in static black holes and dynamical Vaidya spacetimes. It finds that higher-curvature terms add corrections and a competition effect in static cases. In dynamical settings with null shells, complexity growth stays governed by conserved momentum despite velocity jumps at the shell. Gauss-Bonnet corrections extend the critical time in two-sided shocks but keep the logarithmic scrambling time dependence.

Core claim

In Gauss-Bonnet gravity the complete volume proposal leads to explicit higher-curvature corrections for unperturbed black holes that produce a competition effect. For dynamical one-sided and two-sided Vaidya geometries the complexity growth rate remains universally determined by the conserved momentum even though canonical velocities jump across the null shell. The two-sided shock wave analysis further shows that the corrections lengthen the critical time while the scrambling time continues to follow the universal logarithmic law.

What carries the argument

The complete volume proposal for holographic complexity in higher-curvature gravity, which modifies the standard volume by including Gauss-Bonnet curvature contributions to the extremal surface.

If this is right

  • Higher-curvature terms produce a competition effect in the complexity of static Gauss-Bonnet black holes.
  • The complexity growth rate is governed by conserved momentum in one-sided and two-sided Vaidya spacetimes despite velocity jumps.
  • Gauss-Bonnet corrections prolong the critical time for linear growth in shock wave geometries.
  • The logarithmic dependence of the scrambling time remains unchanged under these corrections.

Where Pith is reading between the lines

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

  • This universality implies that key features of holographic complexity may hold beyond Einstein gravity.
  • The extended critical time could influence how quickly information scrambles in stringy black hole models.
  • Similar analyses in other higher-derivative theories might reveal whether momentum governance is a general feature.

Load-bearing premise

The complete volume proposal correctly defines holographic complexity when applied to Gauss-Bonnet gravity in both static and dynamical geometries.

What would settle it

Measuring or computing a complexity growth rate after a null shell that does not match the conserved momentum value in a Gauss-Bonnet Vaidya background would disprove the central claim.

read the original abstract

We investigate the stringy effects on holographic complexity in $(d+1)$-dimensional Gauss-Bonnet gravity using the ``complete volume'' proposal for higher-curvature theories. Our analysis covers unperturbed eternal black holes, as well as the one-sided and two-sided Vaidya spacetimes. The one-sided geometry describes a null shell collapsing into the empty AdS vacuum to form a black hole, while the two-sided geometry represents a null shell injected into an eternal black hole background with arbitrary energy. For unperturbed backgrounds, higher-curvature terms introduce explicit corrections to the standard CV proposal, giving rise to a ``competition effect'' absent in the uncorrected framework. In the dynamical settings, we demonstrate that despite novel jumps in the canonical velocities across the null shell, the complexity growth rate remains universally governed by the conserved momentum, just as in Einstein gravity. Furthermore, our two-sided shock wave analysis reveals that Gauss-Bonnet corrections prolong the critical time, preserving the universal logarithmic dependence for the scrambling time.

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

3 major / 3 minor

Summary. The paper investigates stringy effects on holographic complexity in (d+1)-dimensional Gauss-Bonnet gravity using the complete volume proposal. It analyzes unperturbed eternal black holes, where higher-curvature terms produce a competition effect modifying the complexity, as well as one-sided Vaidya spacetimes (null shell collapsing into AdS to form a black hole) and two-sided Vaidya spacetimes (null shell injected into an eternal black hole). The central results are that, despite novel jumps in canonical velocities across the null shell, the complexity growth rate remains universally governed by the conserved momentum (as in Einstein gravity), and that Gauss-Bonnet corrections prolong the critical time while preserving the universal logarithmic dependence of the scrambling time.

Significance. If the derivations hold, this work is significant for establishing the robustness of key universal features of holographic complexity—momentum-governed growth and logarithmic scrambling times—under higher-curvature corrections in both static and fully dynamical spacetimes. It provides a non-trivial test of the complete volume proposal beyond Einstein gravity and suggests that stringy effects do not disrupt the core information-theoretic relations extracted from the AdS/CFT dictionary. The explicit treatment of one-sided and two-sided shock waves strengthens the case for the proposal's applicability to time-dependent geometries.

major comments (3)
  1. [§2] §2 (complete volume proposal): the adoption of the complete volume as the correct generalization to Gauss-Bonnet gravity is load-bearing for all subsequent claims; the manuscript should explicitly derive or justify why this proposal (rather than alternatives) yields the reported competition effect and the velocity-jump behavior, including the explicit form of the volume functional in the presence of the GB term.
  2. [§4.2] §4.2 (one-sided Vaidya matching): the claim that the growth rate remains governed by the conserved momentum despite jumps in canonical velocities across the null shell is central; the explicit junction conditions and the resulting differential equation for the volume must be shown to reduce to the momentum-governed form without additional assumptions, to confirm it is not an artifact of the proposal.
  3. [§5] §5 (two-sided shock-wave analysis): the statement that GB corrections prolong the critical time while preserving the logarithmic scrambling-time dependence requires the explicit expression for the critical time and its GB dependence; the manuscript should demonstrate that the log form survives non-perturbatively or at least to the order considered, with a clear comparison to the Einstein limit.
minor comments (3)
  1. [Abstract and §1] The abstract and introduction use 'stringy effects' interchangeably with Gauss-Bonnet corrections; a brief remark clarifying that GB is a specific higher-curvature truncation of string theory would help readers.
  2. [§2] Notation for the complete volume functional and the canonical velocities should be introduced with a dedicated equation early in §2 rather than appearing first in the dynamical sections.
  3. [§3] The competition effect in the static case is mentioned but not quantified with a plot or table comparing CV versus complete-volume growth rates; adding such a comparison would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their positive assessment of our work and the constructive comments provided. We have revised the manuscript to include more explicit derivations and expressions as requested.

read point-by-point responses

  1. Referee: [§2] §2 (complete volume proposal): the adoption of the complete volume as the correct generalization to Gauss-Bonnet gravity is load-bearing for all subsequent claims; the manuscript should explicitly derive or justify why this proposal (rather than alternatives) yields the reported competition effect and the velocity-jump behavior, including the explicit form of the volume functional in the presence of the GB term.

    Authors: We justify the use of the complete volume proposal in §2 as it provides the appropriate generalization of the complexity=volume conjecture to higher-derivative gravity theories, consistent with the literature on holographic complexity in GB gravity. The explicit volume functional is derived by including the GB term in the bulk integral, leading to the competition effect from the modified extremization condition. The velocity-jump behavior follows directly from the variation of this functional across the null shell. We have added further details on the derivation of the functional and how it produces these effects in the revised manuscript. revision: yes

  2. Referee: [§4.2] §4.2 (one-sided Vaidya matching): the claim that the growth rate remains governed by the conserved momentum despite jumps in canonical velocities across the null shell is central; the explicit junction conditions and the resulting differential equation for the volume must be shown to reduce to the momentum-governed form without additional assumptions, to confirm it is not an artifact of the proposal.

    Authors: The explicit junction conditions are presented in §4.2, obtained from the continuity requirements on the null shell. The differential equation governing the volume is solved by integrating across the shell, where the GB-induced jumps in velocities are accounted for, but the net growth rate simplifies to being proportional to the conserved momentum due to the structure of the equations of motion. This is not an artifact, as it follows from the same logic as in Einstein gravity but with modified terms that cancel. We have included the full derivation of the reduction in the revised version. revision: yes

  3. Referee: [§5] §5 (two-sided shock-wave analysis): the statement that GB corrections prolong the critical time while preserving the logarithmic scrambling-time dependence requires the explicit expression for the critical time and its GB dependence; the manuscript should demonstrate that the log form survives non-perturbatively or at least to the order considered, with a clear comparison to the Einstein limit.

    Authors: In §5 we obtain the critical time by finding the extremal surface configuration that connects the two sides, resulting in an expression t_c(α) that increases with the GB coupling α. The scrambling time retains its logarithmic dependence on the black hole entropy because the time delay is dominated by the near-horizon region, where the GB corrections modify the coefficient but preserve the log form. This is shown explicitly to first order in α, reducing correctly to the Einstein gravity result when α = 0. We have added the explicit expression for the critical time and the comparison in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper adopts the complete volume proposal as an external input for higher-curvature theories and then applies it to compute complexity in static Gauss-Bonnet black holes and dynamical Vaidya geometries. The reported results—competition effects in the static case, velocity jumps across null shells yet universal momentum governance in the dynamical case, and prolongation of critical time while preserving logarithmic scrambling dependence—follow from explicit matching of the gravitational equations and the volume functional across the shell. No equation or claim reduces by construction to a fitted parameter, self-definition, or prior self-citation chain; the derivations remain independent of the target observables and are presented as direct consequences of the adopted proposal plus the Einstein-Gauss-Bonnet dynamics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the complete volume proposal as the definition of complexity; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption The complete volume proposal is the appropriate generalization of holographic complexity for higher-curvature Gauss-Bonnet gravity.
    Invoked as the foundation for all calculations in unperturbed, one-sided, and two-sided geometries.

pith-pipeline@v0.9.0 · 5476 in / 1240 out tokens · 33222 ms · 2026-05-10T08:43:19.892711+00:00 · methodology

discussion (0)

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