arxiv: 2604.20170 · v1 · submitted 2026-04-17 · ✦ hep-th · gr-qc· quant-ph

Recognition: unknown

Computational Cosmic Censorship

Fuat Berkin Altunkaynak

Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:17 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph

keywords cosmic censorshipholographic complexityAdS/CFTnaked singularitiesReissner-Nordström-AdSWheeler-DeWitt actionGibbons-Hawking-York term

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The pith

Overcharged AdS black holes with naked singularities have divergent holographic complexity.

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

This paper develops a computational version of cosmic censorship using the AdS/CFT correspondence and the complexity equals action proposal. For spacetimes with naked timelike singularities, such as overcharged Reissner-Nordström-AdS, most contributions to the Wheeler-DeWitt action stay finite, but the boundary term at the singularity diverges. The divergence implies infinite holographic complexity, creating an infinite gap even compared to extremal black holes. A general criterion shows this occurs whenever the metric near the origin scales steeper than r to the power of D minus three. If this holds, naked singularities are ruled out because describing them would require infinite computational resources.

Core claim

We evaluate the Wheeler-DeWitt action for overcharged Reissner-Nordström-AdS spacetimes containing naked timelike singularities. The bulk, null, and joint contributions remain finite, while the Gibbons-Hawking-York term at the singularity diverges. For any static and spherically symmetric geometry with near-origin scaling f(r)∼a r^{-p}, the singularity term diverges whenever p>D−3. This implies divergent holographic complexity and leaves an infinite complexity gap relative to the logarithmically divergent extremal charged sector.

What carries the argument

The Gibbons-Hawking-York term in the Wheeler-DeWitt action evaluated at the naked singularity, which diverges for sufficiently steep near-origin metric scaling.

If this is right

The holographic complexity of naked singularities is divergent.
This creates an infinite complexity gap compared to extremal charged black holes.
The divergence occurs for near-origin scalings p > D-3 in static spherical geometries.
Naked singularities are excluded by infinite computational cost from their local structure rather than geometry alone.

Where Pith is reading between the lines

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

This approach might generalize to dynamical or non-spherical spacetimes where similar action divergences could hide singularities computationally.
Complexity could act as an additional physical constraint on allowable spacetimes in quantum gravity.
Future calculations could check if time-dependent naked singularities also produce infinite complexity.

Load-bearing premise

The complexity equals action proposal applies to spacetimes with naked timelike singularities and its divergence corresponds to physically infinite complexity.

What would settle it

Perform the explicit calculation of the Wheeler-DeWitt action for an overcharged Reissner-Nordström-AdS metric with a naked singularity and check if the Gibbons-Hawking-York contribution diverges.

read the original abstract

We propose a computational formulation of weak cosmic censorship in AdS/CFT. Using the complexity=action proposal, we evaluate the Wheeler-DeWitt action for overcharged Reissner- Nordstr\"om-AdS spacetimes containing naked timelike singularities. We show that the bulk, null, and joint contributions remain finite, while the Gibbons-Hawking-York term at the singularity diverges. More generally, for any static and spherically symmetric geometry with near-origin scaling $f(r)\sim a r^{-p}$, the singularity term diverges whenever $p>D-3$. This implies divergent holographic complexity and, even relative to the logarithmically divergent extremal charged sector, leaves an infinite complexity gap. This suggests an operational form of censorship: naked singularities are excluded not by geometry alone, but by an infinite computational cost arising from their local near-singularity structure.

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.

Desk Editor's Note private letter to a colleague

The paper gives a concrete scaling condition for divergent complexity in naked singularities under CA but the physical interpretation rests on shaky ground.

read the letter

The core idea is that overcharged RN-AdS geometries with naked timelike singularities produce a divergent Gibbons-Hawking-York term in the Wheeler-DeWitt action when the near-origin scaling satisfies p > D-3, leaving an infinite complexity gap even against the logarithmically divergent extremal case. This is framed as an operational cosmic censorship: the singularity is excluded because it costs infinite computation. The scaling result and the breakdown showing bulk, null, and joint terms stay finite while only the surface term diverges look like the genuinely new pieces relative to earlier complexity work. The calculation itself is direct and the general static spherical case is cleanly stated. That part earns credit for being explicit and falsifiable in principle. The soft spot is the leap to physical censorship. The CA conjecture is already conjectural in standard settings; extending it to spacetimes where the WDW patch terminates on a naked timelike singularity requires justification that the abstract does not supply. There is no first-principles argument given for why the dictionary survives, no cross-check against CV or CV2.0, and no discussion of whether the divergence survives different regularizations or cutoff choices. If the GHY blow-up is an artifact of how the boundary term is defined near r=0, the infinite-gap claim collapses and the censorship interpretation does not follow. The paper also does not address whether the same divergence appears in other holographic complexity proposals or in known regularized examples. This is for readers already working on holographic complexity and its possible links to classical gravity conjectures. It could interest people who want operational versions of cosmic censorship, but the technical result is preliminary and the interpretation is not yet robust. The math on the action terms is straightforward enough that a serious referee could evaluate the scaling claim and the regularization details quickly. I would send it to peer review rather than desk reject; the new scaling observation is worth referee time even if the broader claim needs substantial revision or additional checks.

Referee Report

2 major / 2 minor

Summary. The paper proposes a computational formulation of weak cosmic censorship in AdS/CFT via the complexity=action (CA) conjecture. For overcharged Reissner-Nordström-AdS geometries containing naked timelike singularities, the Wheeler-DeWitt action is evaluated explicitly; bulk, null, and joint contributions remain finite while the Gibbons-Hawking-York surface term at the singularity diverges. More generally, for any static spherically symmetric metric with near-origin scaling f(r)∼a r^{-p}, the singularity term diverges whenever p>D−3. This produces divergent holographic complexity and an infinite gap relative to the logarithmically divergent extremal sector, suggesting that naked singularities are excluded by infinite computational cost arising from their local structure.

Significance. If the central derivation holds and the CA dictionary remains valid, the work supplies a concrete, falsifiable scaling criterion that links cosmic censorship to divergent complexity. It is one of the few attempts to apply CA to naked singularities and offers a potential operational criterion beyond purely geometric statements. The result is novel but its significance is limited by the absence of cross-checks with other complexity proposals and by the preliminary status of the supporting calculations.

major comments (2)

[Section on Wheeler-DeWitt patch construction and action evaluation] The manuscript assumes without derivation that the standard CA dictionary (Wheeler-DeWitt patch plus action terms) continues to apply when the patch terminates on a naked timelike singularity rather than a horizon. This assumption is load-bearing for the claim of infinite complexity; if the conjecture fails to extend to this regime, the divergence does not translate into a physical computational cost. No independent justification or comparison to the CV proposal is provided.
[General scaling analysis for f(r)∼a r^{-p}] The general scaling result (divergence for p>D−3) is obtained by direct evaluation of the GHY term with a cutoff surface approaching r=0. The paper does not demonstrate that this divergence is independent of the specific regularization scheme or cutoff choice, nor does it compare the outcome against known regularized cases (e.g., extremal RN-AdS or other singular geometries). This leaves open the possibility that the divergence is an artifact of the boundary-term definition.

minor comments (2)

[Abstract and introduction] Notation for the near-origin scaling exponent p and the dimension D should be introduced earlier and used consistently; the abstract states the condition p>D−3 but the main text would benefit from an explicit definition of D at first use.
[Action evaluation for RN-AdS] The manuscript would be strengthened by a brief statement of the precise cutoff procedure used for the GHY term at r=0, including any numerical checks for convergence.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive criticism of our manuscript. We address each major comment below and will revise the paper accordingly to strengthen the discussion of the CA conjecture's applicability and the robustness of the scaling analysis.

read point-by-point responses

Referee: The manuscript assumes without derivation that the standard CA dictionary (Wheeler-DeWitt patch plus action terms) continues to apply when the patch terminates on a naked timelike singularity rather than a horizon. This assumption is load-bearing for the claim of infinite complexity; if the conjecture fails to extend to this regime, the divergence does not translate into a physical computational cost. No independent justification or comparison to the CV proposal is provided.

Authors: We acknowledge that applying the CA conjecture to spacetimes with naked timelike singularities constitutes an extension of the standard formulation, which is typically discussed in the presence of horizons. The Wheeler-DeWitt patch and the associated action terms are defined geometrically, and our explicit evaluation shows that the divergence is isolated to the GHY term at the singularity while bulk, null, and joint contributions remain finite. We will revise the manuscript to add a paragraph in the introduction and Section 2 explaining the rationale for this extension on the basis of the local geometric definitions, while noting that a full derivation of the conjecture in this regime lies beyond the present work. A direct comparison with the CV proposal is also left for future investigation, as it would require separate calculations. revision: partial
Referee: The general scaling result (divergence for p>D−3) is obtained by direct evaluation of the GHY term with a cutoff surface approaching r=0. The paper does not demonstrate that this divergence is independent of the specific regularization scheme or cutoff choice, nor does it compare the outcome against known regularized cases (e.g., extremal RN-AdS or other singular geometries). This leaves open the possibility that the divergence is an artifact of the boundary-term definition.

Authors: The scaling analysis employs a standard radial cutoff at small r=ε, with the GHY term evaluated as ε→0. The divergence for p>D−3 follows directly from the leading power-law behavior of the metric functions in the integral for the extrinsic curvature. We will revise the manuscript to include an explicit demonstration that the result is insensitive to subleading corrections and to the precise shape of the cutoff surface (provided it approaches the origin). We will also add comparisons to the extremal RN-AdS case, where the corresponding term converges, and to other singular geometries in the literature. These clarifications will appear in Section 3 and a new appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is direct evaluation of action terms from metric scaling.

full rationale

The central result follows from explicit computation of the WDW action components (bulk, null, joint, GHY) on the given RN-AdS metric with naked singularity. The divergence condition p > D-3 is obtained by direct integration of the GHY surface term using the near-origin ansatz f(r) ~ a r^{-p}, without fitting parameters or redefinition of inputs. The CA conjecture is invoked as an external assumption from independent prior literature (Brown et al.), not derived or justified via self-citation within this work. No step equates a 'prediction' to a fitted quantity or reduces the claim to a self-referential loop. The paper is self-contained as a calculation once the standard CA dictionary is granted.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the complexity=action conjecture for singular spacetimes and the physical interpretation of action divergence as infinite complexity; no free parameters are introduced in the abstract, but the scaling exponent p and dimension D are treated as given inputs.

axioms (2)

domain assumption The complexity=action proposal equates the Wheeler-DeWitt action to holographic complexity even for spacetimes with naked singularities.
Invoked to interpret the calculated action as complexity.
domain assumption AdS/CFT correspondence provides a valid holographic dual for the complexity calculation.
Foundation for using bulk action to compute boundary complexity.

pith-pipeline@v0.9.0 · 5438 in / 1339 out tokens · 48776 ms · 2026-05-10T07:17:16.125477+00:00 · methodology

discussion (0)

Reference graph

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