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arxiv: 2212.06054 · v3 · pith:BZKSV62Dnew · submitted 2022-12-12 · ⚛️ physics.hist-ph · gr-qc

Geometrization 3.0: the black hole shadow

Juliano C. S. Neves This is my paper

Pith reviewed 2026-05-25 08:59 UTC · model grok-4.3

classification ⚛️ physics.hist-ph gr-qc
keywords geometrization of natureblack hole shadowspacetime symmetryformal causegeneral relativitykinematics-dynamics debate
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The pith

The black hole shadow in general relativity connects spacetime shape directly to dynamics, positioning symmetry as formal cause.

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

The paper identifies three successive geometrizations of nature across history. The third begins with Einstein and is carried forward by the black hole shadow, which ties the geometry of spacetime to its dynamical behavior. This link suggests spacetime symmetry functions as the formal cause behind black hole properties. The argument places this view inside the longstanding kinematics-dynamics discussion in relativity.

Core claim

The third geometrization of nature, which begins with Einstein's general relativity, finds its expression in the black hole shadow phenomenon. That phenomenon relates shape to dynamics. As a consequence, spacetime symmetry could play the role of the formal cause in black hole physics. Spacetime symmetry as formal cause of spacetime could be an interesting point in the kinematics-dynamics debate in the theory of relativity.

What carries the argument

The black hole shadow phenomenon, which supplies the concrete relation between shape and dynamics inside the third geometrization.

Load-bearing premise

The black hole shadow directly elevates spacetime symmetry to the status of formal cause rather than treating it as a descriptive feature already contained in the Einstein equations.

What would settle it

A derivation of the black hole shadow boundary that reproduces all observed properties while treating symmetry strictly as a derived consequence of the field equations rather than an independent formal cause.

Figures

Figures reproduced from arXiv: 2212.06054 by Juliano C. S. Neves.

Figure 1
Figure 1. Figure 1: The shadow of M87* at the center of the Messier 87 gal [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The shadow silhouette for the Kerr black hole for di [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: On the left, the shadow phenomenon described by a di [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

There have been three geometrizations in history. The first one is historically due to the Pythagorean school and Plato, the second one comes from Galileo, Kepler, Descartes and Newton, and the third geometrization of nature begins with Einstein's general relativity. Here the term geometrization of nature means the conception according to which nature (with its different meanings) is largely described by using geometry. In this article, I focus on the third geometrization, in which the black hole shadow phenomenon relates shape to dynamics. As a consequence, spacetime symmetry could play the role of the formal cause in black hole physics. Spacetime symmetry as formal cause of spacetime could be an interesting point in the kinematics-dynamics debate in the theory of relativity.

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 identifies three historical geometrizations of nature and argues that the third, initiated by general relativity, is exemplified by the black hole shadow phenomenon, which relates shape to dynamics; as a consequence, spacetime symmetry is positioned as the formal cause in black hole physics and as a contribution to the kinematics-dynamics debate in relativity.

Significance. If the interpretive framing holds, the essay could enrich philosophical discussions in the history and philosophy of physics by linking the black hole shadow to formal causation and symmetry, though its contribution remains conceptual rather than advancing new derivations, data, or falsifiable predictions.

major comments (1)
  1. [Abstract] Abstract: the claim that the black hole shadow 'relates shape to dynamics' and thereby elevates spacetime symmetry to the status of formal cause is presented as a direct consequence without an independent argument, reference to specific GR solutions (e.g., the Kerr metric), or observational input (e.g., EHT results) that would establish the relation beyond the symmetry already built into the Einstein equations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thoughtful review and constructive suggestion regarding the abstract. The manuscript is a conceptual essay in the history and philosophy of physics rather than a technical derivation, and we will revise the abstract to better indicate the structure of the interpretive argument while preserving its scope.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the black hole shadow 'relates shape to dynamics' and thereby elevates spacetime symmetry to the status of formal cause is presented as a direct consequence without an independent argument, reference to specific GR solutions (e.g., the Kerr metric), or observational input (e.g., EHT results) that would establish the relation beyond the symmetry already built into the Einstein equations.

    Authors: The abstract summarizes the paper's central thesis, which is developed at length in the body through the historical sequence of three geometrizations. The argument proceeds by showing that, within the third geometrization initiated by general relativity, the black hole shadow provides a concrete case in which geometric shape (the boundary determined by null geodesics) is fixed by the spacetime symmetries encoded in exact solutions such as the Kerr metric; this geometric determination in turn governs the observable dynamics of light propagation. The EHT images supply the empirical anchor that makes the symmetry manifest. We acknowledge that the abstract states the conclusion concisely without previewing these steps. We will therefore revise the abstract to include a brief clause referencing the role of the Kerr solution and EHT data, thereby making the logical progression more explicit without altering the essay's interpretive character or adding new technical derivations. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is a short philosophical and historical essay with no equations, no formal derivations, and no predictions or uniqueness theorems. Its central claim is an interpretive suggestion about spacetime symmetry as formal cause, not a derivation that reduces to its own inputs by construction. No self-citations or ansatzes are invoked in a load-bearing technical sense. The argument is self-contained as interpretation and does not meet the criteria for any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard historical accounts of geometrization and the established interpretation of black hole shadows in GR; no new free parameters, invented entities, or ad-hoc axioms are introduced beyond the interpretive claim itself.

axioms (2)
  • domain assumption Nature is largely described by geometry across historical periods
    Invoked in the opening definition of geometrization of nature in the abstract.
  • domain assumption The black hole shadow relates shape to dynamics in GR
    Stated directly in the abstract as the basis for assigning formal-cause status to symmetry.

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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

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