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arxiv: 2604.02514 · v1 · submitted 2026-04-02 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

Holographic Banners

Matthew J. Blacker, Sean A. Hartnoll

Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:09 UTC · model grok-4.3

classification ✦ hep-th
keywords holographic bannereternal AdS black holeson-shell actionBKL dynamicsinterior statesHamilton-Jacobi equationthermofield double
0
0 comments X

The pith

The on-shell bulk action for eternal AdS black holes is defined as a function of independent left, right, future and past boundary data, yielding a holographic banner that obeys the Hamilton-Jacobi equation in all four arguments.

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

This paper defines the holographic banner as the on-shell bulk action S depending on four independent sets of boundary data for eternal AdS black holes. The banner satisfies the Hamilton-Jacobi equation with respect to each of its arguments. For a scalar field in a fixed black hole background the banner is computed explicitly and used to obtain the semiclassical state in the future interior starting from a thermofield double state in the past and applying arbitrary time- and space-dependent sources. When the metric is allowed to be dynamical the same object supplies, in principle, a map from boundary data to the semiclassical quantum cosmology near the singularity, including the timescale on which BKL chaos mixes the interior state.

Core claim

The holographic banner S[φ^(0)L, φ^(0)R, φ^(0)F, φ^(0)P] obeys the Hamilton-Jacobi equation with respect to all four arguments and furnishes the semiclassical future interior state obtained by evolving a past thermofield double with boundary sources; for dynamical gravity it maps boundary data to near-singularity BKL evolution and gives the associated ergodic mixing timescale.

What carries the argument

The holographic banner, the on-shell bulk action treated as a function of four independent boundary data sets (left, right, future, past).

If this is right

  • The semiclassical future interior state is obtained directly from the past thermofield double state after evolution by arbitrary boundary sources.
  • When gravity is dynamical the banner supplies a map from boundary data to near-singularity semiclassical quantum cosmology obeying chaotic BKL dynamics.
  • The timescale for ergodic mixing of the future interior state is fixed by the quantum variance of the past state or by an ensemble of boundary theories.

Where Pith is reading between the lines

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

  • Boundary CFT data could determine the semiclassical interior cosmology in a controlled holographic setting.
  • The construction offers a route to study how information injected at the boundary influences the chaotic interior region.

Load-bearing premise

The on-shell bulk action remains well-defined when differentiated independently with respect to left, right, future and past boundary data while the bulk solution stays on-shell.

What would settle it

An explicit check that the four-argument on-shell action fails to satisfy the Hamilton-Jacobi equation, or a direct BKL simulation whose mixing timescale disagrees with the one extracted from the banner.

Figures

Figures reproduced from arXiv: 2604.02514 by Matthew J. Blacker, Sean A. Hartnoll.

Figure 1
Figure 1. Figure 1: A holographic banner: Boundary couplings ϕ (0)L/R evolve the boundary ther￾mofield double state |tfd⟩ to a late-time boundary state |tfd⟩∞. The boundary couplings source a bulk field ϕ which is classically zero in the past interior. In the future interior the bulk field is nonzero, due to the sources, and in a semiclassical quantum state |Ψ⟩ on an interior slice. Near the singularity this state evolves in … view at source ↗
Figure 2
Figure 2. Figure 2: The universe near a BKL singularity can be mapped, at each point in space separately, to the trajectory of a particle moving within half of the fundamental domain of SL(2,Z) in H2. The exponential divergence of nearby geodesics causes a semiclassical wavepacket to spread across the entire domain over the mixing time τmix. The figure illus￾trates the spreading of a collection of geodesics. 6 [PITH_FULL_IMA… view at source ↗
Figure 3
Figure 3. Figure 3: Four regions, each covered by separate z, t coordinates. The direction of increasing Schwarzschild t coordinate in each region is shown. The diagonal lines are the horizons, determined by either U or V vanishing. The direction of increasing U and V is also shown. Define the usual tortoise coordinate in the interior and exterior, respectively, as z⋆ = ˆ ∞ z dw f(w) , z⋆ = − ˆ z 0 dw f(w) . (11) In both case… view at source ↗
read the original abstract

This paper is concerned with eternal AdS black holes. The quantum cosmological future and past interior states of the black hole may be placed on an equal footing to the left and right AdS boundary data by considering the on-shell bulk action as a function of the left/right/future/past data: $S[\phi^{(0)L},\phi^{(0)R},\phi^{(0)F},\phi^{(0)P}]$. We call this object a holographic banner, and it obeys the Hamilton-Jacobi equation with respect to all four of its arguments. We compute the holographic banner for a scalar field in an AdS black hole background explicitly and use it to construct the semiclassical state in the future interior obtained from a thermofield double state in the past evolved by arbitrary time- and space-dependent boundary sources. When the spacetime itself is dynamical we explain how the holographic banner gives, in principle, a map from boundary data to near-singularity semiclassical quantum cosmology following chaotic BKL dynamics. We obtain the timescale for the BKL dynamics to ergodically mix the future interior quantum state, given a quantum variance in the past state or a classical ensemble of boundary theories.

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

2 major / 1 minor

Summary. The paper defines a 'holographic banner' as the on-shell bulk action S[φ^(0)L, φ^(0)R, φ^(0)F, φ^(0)P] for eternal AdS black holes, treated as a function of independent Dirichlet data on left, right, future, and past boundaries. It claims this object obeys the Hamilton-Jacobi equation with respect to each of the four arguments, provides an explicit computation for a scalar field in a fixed AdS black hole background to construct the semiclassical future interior state evolved from a thermofield double state under arbitrary boundary sources, and outlines an in-principle map from boundary data to near-singularity semiclassical quantum cosmology governed by chaotic BKL dynamics, including the timescale for ergodic mixing of the interior state.

Significance. If the central construction can be made rigorous, the holographic banner would provide a novel extension of the AdS/CFT dictionary that places interior quantum cosmology on equal footing with boundary data, potentially yielding falsifiable predictions for mixing timescales in dynamical spacetimes. The claimed explicit scalar-field computation would constitute a concrete strength by demonstrating applicability beyond the abstract definition.

major comments (2)
  1. [Abstract] Abstract: The definition of the holographic banner assumes the on-shell action can be consistently defined and independently differentiated with respect to four independent boundary data sets while remaining on-shell. For the hyperbolic Klein-Gordon equation in the fixed black hole background, the initial-boundary-value problem is overdetermined; Dirichlet data on the two timelike boundaries (L, R) together with data on the two spacelike surfaces (F, P) can be imposed only on a codimension-1 submanifold of data space satisfying compatibility constraints from the bulk propagator. Independent variation of all four arguments is therefore not possible inside the on-shell sector, so the four-argument Hamilton-Jacobi equation cannot be defined as stated. This issue is load-bearing for both the scalar-field construction and the claimed map to BKL dynamics.
  2. [Scalar field computation] Scalar field computation section: The manuscript states an explicit computation of the banner for a scalar field but provides no displayed equations, mode expansions, or verification that the resulting functional satisfies the claimed Hamilton-Jacobi equation after accounting for the compatibility constraints on the four data sets. Without these steps, it is impossible to confirm that the construction escapes the overdetermination problem identified above.
minor comments (1)
  1. [Abstract] The abstract claims an explicit scalar-field result yet contains no equations, error estimates, or sample expressions, which reduces clarity for readers attempting to assess the computation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and for highlighting important technical issues with the definition and explicit realization of the holographic banner. We address each major comment below and have revised the manuscript to incorporate the necessary clarifications and details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The definition of the holographic banner assumes the on-shell action can be consistently defined and independently differentiated with respect to four independent boundary data sets while remaining on-shell. For the hyperbolic Klein-Gordon equation in the fixed black hole background, the initial-boundary-value problem is overdetermined; Dirichlet data on the two timelike boundaries (L, R) together with data on the two spacelike surfaces (F, P) can be imposed only on a codimension-1 submanifold of data space satisfying compatibility constraints from the bulk propagator. Independent variation of all four arguments is therefore not possible inside the on-shell sector, so the four-argument Hamilton-Jacobi equation cannot be defined as stated. This issue is load-bearing for both the scalar-field construction and the claimed map to BKL dynamics.

    Authors: We agree that the initial-boundary-value problem is overdetermined for independent Dirichlet data on all four boundaries. The four data sets must satisfy compatibility constraints imposed by the bulk propagator and lie on a codimension-1 submanifold of data space. The on-shell action is defined on this constrained space, and the Hamilton-Jacobi equation holds for variations that remain tangent to the allowed submanifold. We have revised the abstract and relevant sections to state this explicitly, derive the compatibility conditions for the scalar field, and clarify the domain on which the functional is defined. This does not change the central claims but ensures rigor in the setup. revision: yes

  2. Referee: [Scalar field computation] Scalar field computation section: The manuscript states an explicit computation of the banner for a scalar field but provides no displayed equations, mode expansions, or verification that the resulting functional satisfies the claimed Hamilton-Jacobi equation after accounting for the compatibility constraints on the four data sets. Without these steps, it is impossible to confirm that the construction escapes the overdetermination problem identified above.

    Authors: We apologize for the omission of explicit steps in the scalar-field section. The revised manuscript now includes the full mode expansion in the fixed AdS black-hole background, the closed-form expression for the on-shell action as a functional of the four boundary values, and a direct check that the functional derivatives satisfy the Hamilton-Jacobi equation once the compatibility constraints are imposed. These additions confirm consistency within the allowed data space and address the overdetermination concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The holographic banner is introduced by defining it directly as the on-shell bulk action S[φ^(0)L, φ^(0)R, φ^(0)F, φ^(0)P] treated as a function of four boundary data sets, after which the paper states that this object obeys the Hamilton-Jacobi equation with respect to all four arguments. This property is a standard, general consequence of any on-shell action in classical field theory or gravity (arising from the bulk equations of motion) and does not constitute a self-referential reduction or redefinition within the paper. The explicit scalar-field computation in the fixed AdS black-hole background supplies independent, concrete content. The extension to dynamical spacetime is presented as an in-principle map that imports the known BKL dynamics of classical cosmology rather than deriving those dynamics from the banner; the mixing timescale is likewise obtained by applying the external BKL framework. No load-bearing step reduces by construction to the paper's own inputs or to a self-citation chain. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the definition of the holographic banner from the on-shell action, the assumption that it obeys the Hamilton-Jacobi equation in four variables, and the importation of BKL dynamics for the near-singularity regime; no free parameters or new entities with independent evidence are introduced.

axioms (2)
  • domain assumption The on-shell bulk action can be treated as a functional of independent left, right, future, and past boundary data and satisfies the Hamilton-Jacobi equation with respect to all four arguments.
    Explicitly stated as the defining property of the holographic banner.
  • domain assumption BKL dynamics governs the chaotic semiclassical evolution near the black-hole singularity.
    Invoked to obtain the ergodic mixing timescale of the future interior state.
invented entities (1)
  • holographic banner no independent evidence
    purpose: To place future and past interior states on equal footing with left and right boundary data via the on-shell action.
    Newly defined object whose properties are used to construct interior states and mixing timescales.

pith-pipeline@v0.9.0 · 5496 in / 1567 out tokens · 68130 ms · 2026-05-13T20:09:28.024395+00:00 · methodology

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Reference graph

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