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arxiv: 2606.06355 · v2 · pith:4DJ7MC6Tnew · submitted 2026-06-04 · 🌀 gr-qc · astro-ph.CO· hep-ph

tt BlackHawk tt v3.0: Hawking Radiation from Regular Black Holes

Alexandre Arbey , Marco Calz\`a , L\'ea Malacher , Davide Pedrotti , Yuber F. Perez-Gonzalez This is my paper

Pith reviewed 2026-06-28 00:03 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-ph
keywords Hawking radiationregular black holesgreybody factorsBlackHawk codespherically symmetric metricsblack hole evaporationnumerical spectra
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The pith

BlackHawk v3.0 adds Hawking radiation calculations for Bardeen, Hayward and other regular black hole metrics.

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

The paper introduces BlackHawk version 3.0 as an updated public code for computing Hawking radiation spectra from black holes. It extends the previous versions by adding support for six new spherically symmetric metrics that include regular black holes without central singularities. For each metric the code now calculates the corresponding Hawking temperature and the greybody factors that shape the emitted particle spectra. These additions allow determination of primary emission rates for particles with different spins. The release also includes technical upgrades to improve numerical precision and computational efficiency while remaining freely available.

Core claim

BlackHawk v3.0 implements the Bardeen and Hayward regular black holes, the Simpson-Visser and Peltola-Kunstatter black-bounces, the D'Ambrosio-Rovelli black hole-to-white hole metric, and the Babichev-Charmousis-Lehébel black hole, together with their Hawking temperatures and greybody factors obtained through dedicated numerical routines from the companion GrayHawk code, thereby enabling primary Hawking emission spectra for particles of different spins in these geometries.

What carries the argument

The implementation of the six new spherically symmetric metrics inside the BlackHawk code, combined with numerical solution of the wave equations via GrayHawk routines to obtain greybody factors for each metric.

If this is right

  • The code can now produce primary Hawking emission spectra for particles of different spins in each of the six new geometries.
  • Hawking temperatures are available for the Bardeen, Hayward, black-bounce, black hole-to-white hole, and Babichev-Charmousis-Lehébel metrics.
  • Technical improvements increase the precision and efficiency of spectrum calculations across all supported metrics.
  • The public code becomes a more versatile tool for studying Hawking radiation from alternative black hole solutions.

Where Pith is reading between the lines

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

  • Researchers could test whether radiation from these regular metrics produces measurable differences from Schwarzschild evaporation at late times.
  • Similar numerical routines might be adapted to additional non-standard metrics if the wave-equation solver proves sufficiently general.
  • Public release of the code could enable community checks of the greybody calculations against analytic limits for the new metrics.

Load-bearing premise

The numerical integration routines solve the wave equations correctly for each new metric without introducing uncontrolled errors or needing unstated metric-specific adjustments.

What would settle it

Compare the greybody factors and emission spectra produced by the updated code for the Schwarzschild metric against results from earlier versions of BlackHawk or independent calculations in the literature.

Figures

Figures reproduced from arXiv: 2606.06355 by Alexandre Arbey, Davide Pedrotti, L\'ea Malacher, Marco Calz\`a, Yuber F. Perez-Gonzalez.

Figure 1
Figure 1. Figure 1: FIG. 1. Temperature dependence on the [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Emission spectra [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Emission photon spectra in the case of Bardeen (left plot) and Hayward (right plot) BHs , assuming a values of [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

We present $\tt BlackHawk$ $\tt v3.0$, a major update of the public code designed to compute Hawking radiation spectra of black holes. Building upon previous versions, this release considerably extends the range of black hole geometries that can be studied by implementing several new spherically symmetric metrics: the Bardeen and Hayward regular black holes, the Simpson-Visser and Peltola-Kunstatter black-bounces, the D'Ambrosio-Rovelli black hole-to-white hole metric, and the Babichev-Charmousis-Leh\'ebel black hole. For each metric, we compute the corresponding Hawking temperatures and greybody factors, enabling the determination of primary Hawking emission spectra for particles of different spins. The greybody factors are obtained through dedicated numerical routines based on the companion code $\tt GrayHawk$. Additionally, $\tt BlackHawk$ $\tt v3.0$ introduces several technical improvements aimed at enhancing precision and efficiency, providing a highly versatile tool. The code is publicly available at https://blackhawk.hepforge.org/

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 / 0 minor

Summary. The manuscript presents BlackHawk v3.0, a major update to the public code for computing Hawking radiation spectra of black holes. It implements several new spherically symmetric metrics (Bardeen and Hayward regular black holes, Simpson-Visser and Peltola-Kunstatter black-bounces, D'Ambrosio-Rovelli black hole-to-white hole metric, and Babichev-Charmousis-Lehébel black hole). For each metric the corresponding Hawking temperatures and greybody factors are computed via dedicated numerical routines based on the companion GrayHawk code, enabling primary emission spectra for particles of different spins. Technical improvements for precision and efficiency are introduced, and the code is released publicly.

Significance. If the numerical implementations are shown to be accurate, the updated code would constitute a useful public resource for studying Hawking radiation from regular and black-bounce geometries that arise in quantum-gravity-motivated models. The public availability and focus on multiple particle spins strengthen its potential utility for the community.

major comments (2)
  1. [Abstract] Abstract: the claim that temperatures and greybody factors are computed for the new metrics is not accompanied by any validation data, convergence tests, or comparisons against known limits (e.g., Schwarzschild). Because the central claim of the paper is the reliable computation of these quantities for non-standard metrics, the absence of such checks is load-bearing.
  2. [Numerical implementation (GrayHawk routines)] The greybody factors are obtained through GrayHawk routines that solve the radial wave equations. The new metrics possess non-standard lapse functions and curvature profiles that alter the effective potential and boundary conditions relative to Schwarzschild; without reported error budgets, coordinate-singularity handling, or cross-checks against independent solvers, it is impossible to confirm that the numerical integration remains controlled for these geometries.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major point below and will revise the manuscript accordingly to strengthen the presentation of the numerical results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that temperatures and greybody factors are computed for the new metrics is not accompanied by any validation data, convergence tests, or comparisons against known limits (e.g., Schwarzschild). Because the central claim of the paper is the reliable computation of these quantities for non-standard metrics, the absence of such checks is load-bearing.

    Authors: We agree that the abstract would be improved by referencing the validation steps performed for the new metrics. In the revised manuscript we will add a concise statement to the abstract noting that the Hawking temperatures and greybody factors have been cross-checked against the Schwarzschild limit and that convergence tests have been carried out. A new subsection in the main text will present representative convergence plots, relative errors, and direct comparisons with the Schwarzschild case for each implemented metric. revision: yes

  2. Referee: [Numerical implementation (GrayHawk routines)] The greybody factors are obtained through GrayHawk routines that solve the radial wave equations. The new metrics possess non-standard lapse functions and curvature profiles that alter the effective potential and boundary conditions relative to Schwarzschild; without reported error budgets, coordinate-singularity handling, or cross-checks against independent solvers, it is impossible to confirm that the numerical integration remains controlled for these geometries.

    Authors: We acknowledge that the current manuscript does not provide a dedicated error analysis for the GrayHawk implementation on the new geometries. In the revised version we will expand the numerical-methods section to include: (i) explicit error budgets obtained from Richardson extrapolation and variation of integration tolerances, (ii) the coordinate choices used to avoid singularities (regular coordinates or horizon-penetrating coordinates), and (iii) comparisons of selected greybody factors against independent numerical solvers or known analytic limits. These additions will be accompanied by tables or figures summarizing the achieved precision for each metric. revision: yes

Circularity Check

0 steps flagged

No circularity: direct code implementation of standard Hawking formulas

full rationale

The paper is a software release note describing the addition of several known regular black hole metrics to an existing numerical code. Hawking temperatures follow from the standard surface gravity formula applied to each metric's lapse function; greybody factors are obtained by numerical integration of the wave equation via the companion GrayHawk routines. No equation is shown to be defined in terms of its own output, no fitted parameter is relabeled as a prediction, and no load-bearing uniqueness claim or ansatz is imported via self-citation. The derivation chain therefore remains self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper introduces no new free parameters, physical axioms beyond standard general relativity, or invented entities. All content is implementation of previously published metrics.

axioms (1)
  • domain assumption Hawking radiation formulas and greybody calculations apply without modification to the listed regular metrics.
    The abstract invokes these formulas directly for the new geometries.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

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