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Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model

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Jose Miguel Ladino, Anuar Idrissov, Carlos E. Romero-Figueroa, Hernando Quevedo

General Relativity and Quantum Cosmology · Submitted 30 Sep 2026 · 190 references

Pith's verdict: The optical half of this paper is solid and worth publishing; the advertised shadow-to-stability connection survives only under the quasi-homogeneous T-convention, which the authors disclose but the abstract oversells.

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CitationAnuar Idrissov, Carlos E. Romero-Figueroa, Hernando Quevedo, Jose Miguel Ladino. "Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model." arXiv:2610.00640 (2026). https://pith.science/paper/XUPD5PXK
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The paper

The paper claims

In the quantum Oppenheimer–Snyder model, a black hole's shadow and photon rings encode its thermodynamic phase: the inner boundary of the first photon ring in the window 5.35M–5.38M marks a thermodynamically stable black hole, while a…

The reading

The paper claims that quantum-corrected Oppenheimer–Snyder (qOS) black holes carry their thermodynamic stability in their images. A measured first photon ring with inner boundary between roughly 5.34570M and 5.38018M would identify a thermodynamically stable qOS black hole, whereas a shadow or ring outside the Davies-threshold value near 5.056M would signal the unstable large-black-hole branch. For the same model, naked singularities produce a bright central ring instead of a dark shadow, because an infinite repulsive core barrier reflects light back, yet they keep photon rings. Their two-ring gap parameters fall outside the Schwarzschild interval for quantum parameter values around 2.32M² and above, giving a concrete observational discriminator. The link between image and thermodynamics runs through the Davies point: at entropy Sₘ ≈ 7.647α̂ the heat capacity diverges and the Geometrothermodynamics (GTD) curvature scalars diverge at exactly the shadow radius r_shm ≈ 5.056M.

What carries the argument

The load-bearing object is the Davies point as a scale-invariant anchor z_m = (1+√13)/6 ≈ 0.7676 in the dimensionless order parameter z = w/r_h, where w = √(r_h² − α̂). At this single value, every geometric observable — the shadow radius r_shm ≈ 5.056M, the photon-ring impact parameters b_nm of Table 2, and the gap parameters Δ_nm — takes a definite value that coincides with the divergence of the heat capacity and of the GTD Ricci scalars. This coincidence is the mechanism that fuses optics to thermodynamics: the common critical state makes a shadow or photon-ring measurement a measurement of the thermodynamic phase.

Extended reading notes

Core claim

Treating the quantum parameter α̂ as a genuine quasi-homogeneous thermodynamic degree of freedom alongside the Bekenstein–Hawking entropy S = πr_h², the paper derives a mass potential M(S,α̂) with conjugate temperature T = ∂M/∂S and Smarr relation M = 2TS + 2Aα̂. The heat capacity C_α̂ diverges at the Davies point S_m = (11+√13)πα̂/6 ≈ 7.647α̂, splitting the black-hole regime into a stable small branch (S < S_m, C_α̂ > 0) and an unstable large branch (S > S_m, C_α̂ < 0). The GTD metric g^II built from the mass and g^I built from the enthalpy both give Ricci scalars that diverge exactly at this Davies point, and the Davies shadow radius is r_shm ≈ 4.4628√α̂ ≈ 5.056M. Because the photon-ring impact parameters b_n and gap parameters Δ_n depend monotonically on entropy, a measured ring or gap places the object on one side of the Davies point, hence into a stability class and a microscopic-interaction phase (attractive/repulsive small, stable; or attractive/repulsive large, unstable).

Load-bearing premise

The optical–thermodynamic map assumes the quantum parameter α̂ is a genuine thermodynamic degree of freedom with the Bekenstein–Hawking entropy and its conjugate temperature T = ∂M/∂S; adopting the surface-gravity temperature instead would move the Davies point and reshuffle the classification.

Editorial extensions

If this is right

  • Future high-resolution observations resolving the n = 1 photon ring, as targeted by the Black Hole Explorer concept, could distinguish qOS black holes from Schwarzschild and from other modified-gravity compact objects by the ring's boundary position.
  • The gap parameter Δ_n gives a mass-independent, emission-model-robust test of the background geometry: a measured relative separation between consecutive photon rings falling outside the predicted qOS interval would rule out the qOS metric even without knowing the disk emission radius.
  • qOS naked singularities that retain photon and anti-photon spheres can be told apart from black holes by a bright central ring replacing the dark inner shadow, with gap intervals strictly distinct from Schwarzschild at α̂ = 2.32M².
  • Shadow and photon-ring data classify a qOS black hole into the stable small or unstable large thermodynamic branch and into attractive or repulsive microscopic-interaction phases, so imaging becomes a probe of black-hole thermodynamics.
  • The thermodynamic results, including the Davies point location and the resulting optical classification, refer specifically to the Bekenstein–Hawking entropy and its conjugate temperature adopted in Sec. 2.2.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the Davies-point location depends on the entropy–temperature convention, a high-precision shadow or ring measurement near the 5.056M threshold would discriminate between the Bekenstein–Hawking-conjugate temperature adopted here and the surface-gravity temperature that (per the paper's own remark) requires a logarithmically corrected entropy — a testable way to pick the thermodynamic scheme
  • The optical-to-stability map is generic to any two-parameter quasi-homogeneous black hole whose GTD curvature shares a Davies-type anchor with the shadow; the same framework could plausibly be extended to other LQG-corrected or hair-carrying geometries, although the paper itself only applies it to qOS.
  • The naked-singularity sector is left without a thermodynamic readout; if a quantum-gravity entropy model for a Planck-size singular core is ever established, the gap-parameter intervals computed here could be reinterpreted as the thermal map that the present horizon-based framework cannot provide.
Original abstract

We investigate the optical and thermodynamic properties of quantum Oppenheimer-Snyder (qOS) spacetimes in both the black hole and naked singularity regimes. By analyzing test-particle motion and employing numerical ray tracing of thin accretion disk models, we identify their characteristic optical signatures. We find that increasing the quantum correction parameter reduces the apparent shadow size. While qOS black holes exhibit dark inner shadows, naked singularities produce central bright rings, driven by an infinite repulsive core barrier, yet still retain key optical features such as photon rings. Furthermore, using a semi-analytical approach, we obtain higher-order photon-ring impact and gap parameters that closely align with our numerical findings. Notably, the gap parameter intervals for qOS naked singularities deviate from the Schwarzschild case, providing a concrete criterion for observational tests. Finally, in the black-hole sector, the application of Geometrothermodynamics (GTD) identifies the specific-heat divergence at the Davies point. By linking photon-ring observables to GTD curvature scalars, we reveal a direct connection between qOS black hole shadows, thermodynamic stability, and microscopic interaction structures.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-02: 1 request, 6,287 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.47 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.85 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We investigate the optical and thermodynamic properties of quantum Oppenheimer-Snyder (qOS) spacetimes in both the black hole and naked singularity regimes. By analyzing test-particle motion and employing numerical ray tracing of thin accretion disk models, we identify their characteristic optical signatures. We find that increasing the quantum correction parameter reduces the apparent shadow size. While qOS black holes exhibit dark inner shadows, naked singularities produce central bright rings, driven by an infinite repulsive core barrier, yet still retain key optical features such as photon rings. Furthermore, using a semi-analytical approach, we obtain higher-order photon-ring impact and gap parameters that closely align with our numerical findings. Notably, the gap parameter intervals for qOS naked singularities deviate from the Schwarzschild case, providing a concrete criterion for observational tests. Finally, in the black-hole sector, the application of Geometrothermodynamics (GTD) identifies the specific-heat divergence at the Davies point. By linking photon-ring observables to GTD curvature scalars, we reveal a direct connection between qOS black hole shadows, thermodynamic stability, and microscopic interaction structures.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate the optical and thermodynamic properties of quantum Oppenheimer-Snyder (qOS) spacetimes in both the black hole and naked singularity regimes. contribution 0.98 0.86 0.06 asserted 0.75
s1 By analyzing test-particle motion and employing numerical ray tracing of thin accretion disk models, we identify their characteristic optical signatures. method 0.99 0.95 0.03 asserted 1.00
s2 We find that increasing the quantum correction parameter reduces the apparent shadow size. result 1.00 0.95 0.14 asserted 1.00
s3 While qOS black holes exhibit dark inner shadows, naked singularities produce central bright rings, driven by an infinite repulsive core barrier, yet still retain key optical features such as photon rings. result 0.98 0.92 0.32 asserted 1.00
s4 Furthermore, using a semi-analytical approach, we obtain higher-order photon-ring impact and gap parameters that closely align with our numerical findings. result 0.66 0.96 0.08 asserted 1.00
s5 Notably, the gap parameter intervals for qOS naked singularities deviate from the Schwarzschild case, providing a concrete criterion for observational tests. result 0.70 0.86 0.16 asserted 1.00
s6 Finally, in the black-hole sector, the application of Geometrothermodynamics (GTD) identifies the specific-heat divergence at the Davies point. result 0.69 0.92 0.09 asserted 1.00
s7 By linking photon-ring observables to GTD curvature scalars, we reveal a direct connection between qOS black hole shadows, thermodynamic stability, and microscopic interaction structures. interpretation 0.81 0.94 0.56 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.55 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Radii rh, rph, rsh, and rISCO in (a) parameter and (b) entropy spaces for the quantum Oppenheimer-Snyder spacetime. Stable and unstable black hole and naked singularity regions are shown. Red dots mark the Davies point, with rhm, rphm, rshm, and rISCOm denoting the corresponding radii; blue dots indicate the extremal case. Gray dots in (a) mark where the photon sphere and critical shadow cease to exist for naked singularities
Figure 2. Impact parameter configurations on the observer’s screen with celestial coordinates α(M) and β(M), showing the black hole and photon rings. (a) Impact parameter bn(φ) for the n-th ring. (b) For θ0 = 0◦ , the rings are concentric, with constant gap ∆bn between bn and bn+1. (c) For θ0 > 0 ◦ , the rings deform and bn(φ) depends on φ, while ∆bn is conserved at φ ∈ {0 ◦ , 180◦}, making it optimal to measure ∆n defined in Eq. (48). Adapted from [65]. To simulate the shadow images, we adopt three toy model emission profiles Iem(r) (M = 1) [149–153]: • Profile 1: second-order decay startin
Figure 3. Shadow images generated using Profile 1 from rISCO in Eq. (39) at various observer inclinations, from left to right: θ0 = 0◦ , 17◦ for M87*, 30◦ for Sgr A*, and 80◦ . Top row: Schwarzschild black holes. Center row: Extremal qOS black holes. Bottom row: qOS naked singularities. these inner rings can be highly intense, potentially con￾stituting the brightest region of the entire image. This effect is strikingly evident for Profile 3 (Figs. 7 and 8): as θ0 increases, strong gravitational lensing forces lines of sight to spiral deeply and cross the equatorial disk multiple times.…
Figure 4. Zoomed-in view of the direct image b0 and photon rings bn≥1 for the configurations in
Figure 5. Shadow images generated using Profile 2 from rph in Eq. (40) at various observer inclinations, from left to right: θ0 = 0◦ , 17◦ for M87*, 30◦ for Sgr A*, and 80◦ . Top row: Schwarzschild black holes. Center row: Extremal qOS black holes. Bottom row: qOS naked singularities. boundaries b in 1 ∈ (5.34570M, 5.47892M) and b out 1 ∈ (6.09538M, 6.16755M), this observation could serve as a direct benchmark to distinguish the qOS model from General Relativity and alternative gravitational theories. 3.3 Semi-Analytical Photon Rings Following [65, 66], we calculate the photon-ring impact…
Figure 6. Zoomed-in view of the direct image b0 and photon rings bn≥1 for the configurations in
Figure 7. Shadow images generated using Profile 3 from rh in Eq. (41) at various observer inclinations, from left to right: θ0 = 0◦ , 17◦ for M87*, 30◦ for Sgr A*, and 80◦ . Top row: Schwarzschild black holes. Center row: Extremal qOS black holes. Bottom row: qOS naked singularities (assuming r = 0.05M in place of rh in Eq. (41) ). evaluated with η = 1 − rph/r as kO = Z 1− rph r0 0 G(η)dη, kS = Z 1− rph rS 0 G(η)dη, (45) and G = G(η) given by G = r 2 q ph r 4 ph − 9M2αˆ s 9M2αˆ − r 4 ph ηQ − r 2 ph |η| q r 4 ph − 9M2αˆ , (46) Q = r 4 ph(η − 2) + 2Mr3 ph(η
Figure 8. Zoomed-in view of the direct image b0 and photon rings bn≥1 for the configurations in
Figure 9. Behavior of the impact parameter b2 for qOS spacetime. Panels (a,c) show b2 versus αˆ for varying θ0 and screen polar angle φ, respectively, while (b,d) show the corresponding entropy-space results. Unstable and stable black holes and naked singularities are indicated. Red dots (b2m) mark the Davies point, and blue dots the extremal case. ∆n = 2(rS − rph)(r 4 ph − 9M2αˆ) × ( 2(rS − rph)(r 4 ph − 9M2αˆ) × exp   q r 4 ph − 9M2αˆ r 2 ph
Figure 10. Intervals of the gap parameter ∆2, measuring the relative separation between the n = 2 and n = 3 photon rings, obtained by varying rS from rISCO to infinity using Eq. (49). In (a), ∆2 is compared for Schwarzschild, qOS, and extremal qOS black holes, and naked singularities. In (b), ∆2 is shown versus αˆ, with the corresponding MTPs; small phases are thermodynamically stable. AS, RS, AL, and RL denote Attractive Small, Repulsive Small, Attractive Large, and Repulsive Large phases, respectively. observables to the thermodynamic structure, with the Davies point (T = Tm) separating…

Figures reproduced from arXiv:2610.00640 by the authors.

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