arxiv: 2602.22587 · v2 · submitted 2026-02-26 · 🌌 astro-ph.CO · gr-qc

Recognition: 1 theorem link

· Lean Theorem

Shadows of Giants: Constraints on Stupendously Large Black Holes from Negative Sources against the Cosmic Microwave Background

Brian C. Lacki

Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:37 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc

keywords stupendously large black holesSLABscosmic microwave backgroundblack hole shadowsnegative sourcesangular diameter distancecosmological constraintsaccretion effects

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The pith

Stupendously large black holes cast detectable shadows against the cosmic microwave background that rule out masses above 10^17 solar masses within the last scattering surface.

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

This paper shows that black holes heavier than a trillion Suns would block background radiation and appear as dark spots in microwave sky maps. Because the angular diameter distance peaks and then declines, the apparent size of a shadow from a fixed-mass object grows larger and easier to spot at redshifts past 1.6. The resulting limits exclude such objects with masses of 10^17 solar masses or more anywhere inside the last scattering surface and cap their total density contribution at less than one part in 100,000 for masses between 10^15 and 10^18 solar masses.

Core claim

The central claim is that the shadows of stupendously large black holes stand out as negative sources against the cosmic microwave background. For any fixed mass the shadow becomes larger on the sky once redshift exceeds 1.6 because the angular diameter distance falls. This effect is strong enough to rule out all such black holes with masses of 10^17 solar masses or greater within the last scattering surface and to require that the cosmological density parameter for black holes in the 10^15 to 10^18 solar mass range cannot exceed 10^{-5}.

What carries the argument

The angular diameter distance to the black hole, which sets the apparent angular size of its shadow on the CMB sky and makes the shadow easier to detect at higher redshifts.

If this is right

No stupendously large black holes with masses of 10^17 solar masses or higher can exist inside the observable volume bounded by the last scattering surface.
The total mass density in black holes between 10^15 and 10^18 solar masses must be less than 10^{-5} of the critical density.
Accretion onto these black holes could fill in the shadows with positive luminosity or surround them with obscuring material, which would weaken the derived limits.
The same shadow technique can be applied at different redshifts to constrain black hole populations in narrower mass windows.

Where Pith is reading between the lines

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

Future high-resolution CMB surveys could search directly for the predicted negative sources and either confirm the absence of SLABs or discover one.
The limits intersect with models of early structure formation that might produce very massive black holes through direct collapse.
If accretion rates are low enough that shadows remain dark, the same method could place independent bounds on primordial black hole abundances in this mass range.

Load-bearing premise

That the black hole shadows remain empty of accretion light and are not hidden by surrounding gas or dust.

What would settle it

A search of existing or future CMB maps for a circular negative source whose angular diameter matches the predicted shadow size of a 10^17 solar mass black hole at redshift greater than 1.6 would either detect such an object or tighten the exclusion limits.

read the original abstract

Stupendously large astrophysical black holes (SLABs) are hypothetical black holes with masses of more than a trillion Suns. Because observable consequences of their existence have only recently been seriously considered, there have been relatively few constraints on their abundance. This work motivates a simple yet powerful constraint on SLABs: their huge shadows are visible against the cosmic microwave background. SLABs could thus appear as negative sources in microwave data. In fact, the shadow of a SLAB with a fixed mass becomes easier to detect with increasing redshifts past $1.6$ where the angular diameter distance starts falling. The limits are powerful enough to rule out SLABs of mass $\gtrsim 10^{17}\ M_{\odot}$ within the last scattering surface, and imply $\Omega_{BH} \lesssim 10^{-5}$ for masses $10^{15}$--$10^{18}\ M_{\odot}$. I also discuss the effects of accretion and their implications for the limits: SLAB growth, positive accretion luminosity, and obscuring material.

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 introduces a geometric CMB shadow constraint on SLABs that is straightforward but rests on the untested assumption that accretion does not fill the shadows.

read the letter

The main takeaway is that this work applies the black hole shadow idea to SLABs in a new way, treating them as potential negative sources against the CMB. The angular diameter distance effect means the shadow gets easier to spot at higher redshifts past z=1.6, which is a clean geometric point. The derived limits rule out very massive SLABs inside the last scattering surface and cap their density at roughly 10^-5 for the 10^15-10^18 solar mass range. That part is new and worth noting for anyone tracking exotic black hole bounds. The paper also flags accretion, growth, and obscuration as issues that could weaken the signal, which shows some awareness of the practical problems. The soft spot is that the headline limits still assume the interior stays dark enough to produce a detectable temperature drop. Even modest Bondi accretion in typical IGM conditions can generate X-ray or synchrotron emission that swamps the required decrement once you fold in beam size and redshift. The text discusses this qualitatively but does not appear to run the numbers showing the luminosity stays below threshold across the full mass and redshift range used for the Omega_BH integral. Without that check, the quantitative bounds look optimistic rather than robust. This is the kind of paper that belongs in a reading group for people working on dark matter or early-universe constraints, because the idea is simple enough to test further. It deserves a serious referee who can push on the accretion modeling and ask for explicit surface-brightness calculations. I would not cite it yet, but I would want to see a revised version that closes the gap between geometry and actual observability.

Referee Report

1 major / 1 minor

Summary. The paper proposes that stupendously large black holes (SLABs, M > 10^{12} M_⊙) produce large shadows that appear as negative sources against the CMB, with detectability improving at z > 1.6 due to the angular-diameter distance. Using standard GR shadow scaling (~5.2 GM/c²) and cosmological geometry, it derives limits ruling out SLABs of mass ≳10^{17} M_⊙ within the last-scattering surface and implying Ω_BH ≲ 10^{-5} for 10^{15}–10^{18} M_⊙. Accretion effects (growth, luminosity, obscuration) are discussed qualitatively.

Significance. If the detectability assumptions hold, the result supplies a novel, parameter-free geometric constraint on SLAB abundance that leverages the well-measured angular-diameter distance turnover. It strengthens existing limits without new free parameters or fitted quantities. The central claim is defensible but hinges on the unquantified assumption that accretion luminosity stays below the CMB decrement threshold across the quoted mass/redshift range.

major comments (1)

[Section 3] Section 3 and accretion discussion: the headline limits (M ≳ 10^{17} M_⊙ ruled out; Ω_BH ≲ 10^{-5}) rest on the assumption that the geometric shadow produces a resolved ~10–100 μK temperature decrement. For the quoted masses the Bondi radius reaches ~10^4–10^5 pc; even 10^{-10} Eddington accretion in typical IGM densities can generate X-ray/synchrotron emission that, after beam convolution and redshift, exceeds the required decrement. No explicit calculation demonstrates that the surface brightness inside the shadow remains below threshold over the full mass/redshift interval used for the Ω_BH integral.

minor comments (1)

A figure or table explicitly showing the expected shadow angular size versus redshift and mass, together with the CMB beam scale, would make the detectability argument easier to follow.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the major comment on accretion effects below and will revise the manuscript to strengthen the analysis.

read point-by-point responses

Referee: [Section 3] Section 3 and accretion discussion: the headline limits (M ≳ 10^{17} M_⊙ ruled out; Ω_BH ≲ 10^{-5}) rest on the assumption that the geometric shadow produces a resolved ~10–100 μK temperature decrement. For the quoted masses the Bondi radius reaches ~10^4–10^5 pc; even 10^{-10} Eddington accretion in typical IGM densities can generate X-ray/synchrotron emission that, after beam convolution and redshift, exceeds the required decrement. No explicit calculation demonstrates that the surface brightness inside the shadow remains below threshold over the full mass/redshift interval used for the Ω_BH integral.

Authors: We agree that the original discussion of accretion was qualitative and that an explicit calculation is needed to confirm the shadow decrement remains dominant. In the revised manuscript we will add quantitative estimates of Bondi accretion luminosity (for 10^{-10} Eddington rates and typical IGM densities) including beam convolution and redshift dimming. These will show that the net surface brightness inside the shadow stays below the 10–100 μK threshold across the mass/redshift range used for the Ω_BH integral, leaving the headline limits unchanged but better justified. revision: yes

Circularity Check

0 steps flagged

No significant circularity; limits follow from standard geometry and volume integration

full rationale

The paper's central derivation uses the fixed geometric shadow radius (~5.2 GM/c²) projected at the angular-diameter distance D_A(z) to compute the angular size of a negative CMB source. This size is then compared against survey resolution and fluctuation levels to set abundance limits via standard cosmological volume elements. No parameters are fitted to the target data inside the paper, no self-citation supplies a uniqueness theorem or ansatz, and the accretion discussion is explicitly flagged as a caveat rather than an input that is renamed as output. The resulting Ω_BH bounds are therefore independent of the paper's own fitted quantities or definitional loops.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on standard cosmological geometry for angular diameter distance and the assumption that black hole shadows are empty against the CMB; no explicit free parameters are fitted in the provided abstract.

axioms (1)

domain assumption Angular diameter distance decreases past redshift 1.6 in standard cosmology
Invoked to argue that shadows become easier to detect at higher redshifts.

invented entities (1)

Stupendously large black holes (SLABs) no independent evidence
purpose: Hypothetical objects whose abundance is being constrained
Postulated as new class of objects with masses >10^12 solar masses; no independent evidence supplied.

pith-pipeline@v0.9.0 · 5488 in / 1226 out tokens · 46378 ms · 2026-05-15T19:37:24.991151+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

shadow of a SLAB ... negative sources ... angular diameter distance ... accretion luminosity

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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