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arxiv: 2412.05072 · v2 · submitted 2024-12-06 · 🌀 gr-qc

Signatures of a de Sitter-core black hole in ringing, transmission and optical appearance

N.Heidari , A. A. Ara\'ujo Filho , V. Vertogradov and , A. \"Ovg\"un This is my paper

Pith reviewed 2026-05-23 07:48 UTC · model grok-4.3

classification 🌀 gr-qc
keywords de Sitter core black holequasinormal modesgreybody factorsHawking radiationblack hole shadowscalar perturbationsanisotropic stress tensor
0
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The pith

A black hole with a larger de Sitter core shifts its quasinormal spectrum, strengthens greybody filtering, lowers Hawking temperature, and mildly shrinks its shadow.

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

The paper studies a static, asymptotically flat black hole whose interior approaches de Sitter vacuum, controlled by ADM mass M0 and core scale R. It shows that raising R lowers the peak of the scalar effective potential, moves the quasinormal frequencies and damping times away from the Schwarzschild values (most noticeably at low multipoles and higher overtones), increases the suppression of transmission probabilities, reduces the Hawking temperature, and produces a slightly smaller apparent shadow in ray-traced images of infalling matter. These effects follow from the metric generated by an exponentially decaying anisotropic stress-energy source that interpolates between the core and the exterior.

Core claim

Increasing the core scale R lowers the peak of the scalar effective potential, shifts the quasinormal spectrum away from Schwarzschild, strengthens greybody filtering, decreases Hawking temperature, and mildly reduces the apparent shadow size, with the largest fractional deviations for low multipoles and higher overtones.

What carries the argument

The de Sitter-core geometry generated by an exponentially decaying anisotropic source, parametrized by ADM mass M0 and core scale R, that produces two horizons merging at R/M0 approximately 0.7768.

If this is right

  • Two horizons exist for R below the critical value and merge into an extremal configuration at R/M0 approximately 0.7768.
  • The QNM-greybody correspondence provides a complementary estimate of transmission probability in the eikonal regime.
  • Hawking emission is suppressed and its spectrum shifts to lower frequencies as the core enlarges.
  • Ray-traced intensity profiles show reduced shadow radius and brightness for optically thin infalling flows.

Where Pith is reading between the lines

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

  • If such cores exist, they would produce observable deviations in gravitational-wave ringdown signals from stellar-mass black holes at low multipoles.
  • The model suggests that shadow measurements alone may not tightly constrain the core scale, but combined with ringdown data they could.
  • The construction could be tested by checking whether the same source term yields consistent thermodynamics across different field perturbations.

Load-bearing premise

The geometry is produced by imposing an exponentially decaying anisotropic source whose stress tensor yields an asymptotically flat exterior and de Sitter interior, without derivation from a fundamental action.

What would settle it

High-precision measurements of quasinormal mode frequencies for a black hole of known mass that match the predicted shifts for a given R would support the model; systematic absence of such shifts in ringdown data from multiple events would falsify it.

Figures

Figures reproduced from arXiv: 2412.05072 by A. A. Ara\'ujo Filho, A. \"Ovg\"un, N.Heidari, V. Vertogradov and.

Figure 1
Figure 1. Figure 1: The Lapse function for Schwarzschild BH with a dashed line and the black hole with the de Sitter core for various values of R/M0. According to the lapse function represented in Eq. (2.10), In the next section, we will examine the impact of the de Sitter parameter on the QNMs of the black hole. As it has already been noted, the metric (2.2) describes both singular and regular black holes. How￾ever, as point… view at source ↗
Figure 2
Figure 2. Figure 2: The effective potential is shown for l = 1. The Dashed line corresponds to the Schwarzschild BH and the colored lines are devoted to the black hole with de Sitter core with different values of R/M0. 4 Quasinormal Modes The semi-analytical approach of WKB is a valuable method for the calculation of the QNMs. However, due to the complexity of the lapse function in the nu￾merical approach, the third–order WKB… view at source ↗
Figure 3
Figure 3. Figure 3: The real and imaginary terms of QNMs for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Normalized deviation of the real and imagi [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The greybody bound for different R/M0 val￾ues. We can observe that the greybody factors of a black hole with de Sitter core are smaller when the frequency is fixed, and the de Sitter parameter increases, which demonstrates that the probability of Hawking radiation reaching spatial infinity is greater when the effect of the de Sitter core has a stronger effect. 6 Correspondence between greybody factors and … view at source ↗
Figure 7
Figure 7. Figure 7: Greybody factor for the gravitational pertur [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Emission rate of a Schwarzschild black hole [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temperature versus the horizon radius for Schwarzschild black hole with dashed line and Schwarzschild black hole with the de Sitter core with color lines. The temperature concerning horizon radius is demonstrated in [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Left column: intensity distribution plots of [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
read the original abstract

We investigate a static, asymptotically flat black hole whose central region approaches a de Sitter vacuum. The geometry is controlled by the ADM mass $M_0$ and a core scale $R$, and is generated by an exponentially decaying anisotropic source. After clarifying the stress tensor and the horizon structure, we study scalar-field perturbations, greybody transmission, Hawking emission and the optical image produced by an optically thin infalling flow. The horizon analysis shows that two horizons exist below the critical value $R/M_0\simeq0.7768$, where they merge into an extremal configuration. Increasing the core scale lowers the peak of the scalar effective potential and shifts the quasinormal spectrum away from the Schwarzschild value, with the largest fractional deviations occurring for low multipoles and higher overtones within the WKB domain of validity. The greybody bound indicates stronger filtering as the core becomes more extended, while the QNM--greybody correspondence gives a complementary estimate of the transmission probability in the eikonal regime. The Hawking temperature decreases as the extremal configuration is approached, suppressing the emission rate and shifting its maximum to lower frequencies. Finally, ray-traced intensity profiles show that the apparent shadow and brightness distribution are mildly reduced by a larger de Sitter core.

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 / 2 minor

Summary. The manuscript constructs a static, asymptotically flat black hole with a de Sitter core controlled by ADM mass M0 and core scale R, generated by an exponentially decaying anisotropic stress-energy source. After determining the horizon structure (two horizons merge at critical R/M0 ≃ 0.7768), it computes scalar quasinormal modes via WKB, greybody transmission factors, Hawking temperature and spectrum, and the optical appearance via ray-tracing of an optically thin infalling flow, reporting that larger R lowers the effective potential peak, shifts the QNM spectrum (largest fractional changes at low multipoles and higher overtones), strengthens greybody filtering, suppresses and redshifts Hawking emission, and mildly reduces the apparent shadow size.

Significance. If the numerical results hold, the paper supplies concrete, reproducible trends for how a tunable de Sitter core modifies standard black-hole observables within an explicitly defined two-parameter family. The use of established techniques (WKB for QNMs, ray-tracing for images) and the direct mapping from R to each observable constitute a useful benchmark for phenomenological regular-black-hole models, even though the source is imposed rather than derived from an action.

major comments (2)
  1. [Abstract and horizon-structure section] Abstract and horizon-structure section: the critical ratio R/M0 ≃ 0.7768 is reported as the merger point without the explicit metric function f(r), the horizon equation, the numerical root-finding algorithm, or any convergence/error estimate; this value is load-bearing for all subsequent extremal-limit statements.
  2. [Scalar perturbations and WKB section] Scalar perturbations and WKB section: the claim that fractional deviations are largest for low multipoles and higher overtones rests on WKB results, yet no table of explicit frequencies (or comparison to Schwarzschild values) is referenced, nor is the domain of WKB validity quantified for the reported overtones; without these the quantitative shifts cannot be assessed independently.
minor comments (2)
  1. The functional form and decay constant of the anisotropic source are stated to be chosen to enforce the desired interior/exterior behavior, but the explicit expression for the stress tensor components is not reproduced in the abstract; including it (or a reference to the defining equation) would improve reproducibility.
  2. The greybody-bound and QNM–greybody correspondence statements would benefit from a brief statement of the frequency range or multipole range over which each approximation is applied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the recommendation for minor revision. We address the two major comments below and will incorporate the requested details and data into the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and horizon-structure section] Abstract and horizon-structure section: the critical ratio R/M0 ≃ 0.7768 is reported as the merger point without the explicit metric function f(r), the horizon equation, the numerical root-finding algorithm, or any convergence/error estimate; this value is load-bearing for all subsequent extremal-limit statements.

    Authors: We agree that the horizon-structure analysis requires additional explicit documentation to support the reported critical ratio. In the revised manuscript we will add the explicit metric function f(r), the horizon equation, a description of the numerical root-finding algorithm, and convergence/error estimates for the value R/M0 ≃ 0.7768. revision: yes

  2. Referee: [Scalar perturbations and WKB section] Scalar perturbations and WKB section: the claim that fractional deviations are largest for low multipoles and higher overtones rests on WKB results, yet no table of explicit frequencies (or comparison to Schwarzschild values) is referenced, nor is the domain of WKB validity quantified for the reported overtones; without these the quantitative shifts cannot be assessed independently.

    Authors: We agree that a table of explicit frequencies and a quantification of the WKB validity domain would allow independent assessment. The revised manuscript will include a table of quasinormal frequencies with direct comparisons to the Schwarzschild case for representative multipoles and overtones, together with an explicit discussion of the WKB validity range used for the reported results. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper defines a two-parameter metric (M0, R) with an anisotropic source imposed by construction to enforce a de Sitter interior and asymptotically flat exterior. All subsequent results—QNM shifts via WKB, greybody factors, Hawking temperature, and ray-traced shadows—are direct numerical evaluations on this fixed background using standard methods. No step reduces a claimed prediction to a fitted input, self-citation chain, or definitional tautology; the dependence on R is the model's explicit content rather than a hidden reduction. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The model rests on an imposed stress-energy source whose functional form is chosen to realize the desired interior; no independent derivation or observational anchor is given for this source.

free parameters (2)
  • core scale R
    Free parameter controlling the size of the de Sitter region; all reported deviations scale with R/M0.
  • ADM mass M0
    Overall mass scale; results are presented in units of M0.
axioms (2)
  • domain assumption Einstein equations hold with the chosen anisotropic stress-energy tensor
    Standard general-relativity assumption invoked to generate the metric from the source.
  • standard math The spacetime is static and spherically symmetric
    Background assumption used throughout the perturbation and ray-tracing analysis.
invented entities (1)
  • exponentially decaying anisotropic source no independent evidence
    purpose: Generates the metric that interpolates between de Sitter core and Schwarzschild exterior
    New stress-energy distribution postulated to produce the desired geometry; no independent evidence supplied.

pith-pipeline@v0.9.0 · 5778 in / 1569 out tokens · 22378 ms · 2026-05-23T07:48:29.551837+00:00 · methodology

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