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arxiv: 2605.09756 · v1 · submitted 2026-05-10 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Hawking Radiation and Greybody Factors of Test Scalar and Electromagnetic Fields on Asymptotically Flat Pure Lovelock Black Holes

Jayden Tan

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:17 UTC · model grok-4.3

classification 🌀 gr-qc
keywords pure Lovelock black holesHawking radiationgreybody factorsscalar fieldselectromagnetic fieldshigher dimensionscritical branch
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The pith

Pure Lovelock black holes radiate far less Hawking radiation than Schwarzschild-Tangherlini black holes of the same horizon radius because their lower temperature outweighs higher wave transmission.

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

Pure Lovelock black holes in the critical branch d=2N+2 have metrics that transmit scalar and electromagnetic waves more readily than Einstein-gravity black holes. Their Hawking temperatures are nevertheless lower, so the net radiated power drops sharply. In the benchmark six-dimensional case the integrated scalar power falls by roughly three orders of magnitude and the electromagnetic power by five. The paper further shows that raising the Lovelock order N makes the electromagnetic sector increasingly dominated by its scalar-type polarization.

Core claim

We compute scalar and higher-dimensional electromagnetic greybody factors and Hawking spectra on the critical branch d=2N+2, compare them with Schwarzschild-Tangherlini black holes at the same horizon radius r_h, and show that the smaller Hawking temperature overwhelms the enhanced transmission. In the benchmark d=6 case, the integrated scalar and electromagnetic powers are reduced by about 10^{-3} and 10^{-5}, respectively. We also find a clean higher-curvature signature: as the Lovelock order N grows, Hawking radiation becomes increasingly dominated by the scalar-type electromagnetic sector.

What carries the argument

Greybody factors obtained by solving the radial wave equations for massless scalar and electromagnetic test fields on the pure Lovelock metric and folding the transmission probabilities into the Planck spectrum.

If this is right

  • In six dimensions the total scalar Hawking power is suppressed by a factor of roughly 10^{-3} relative to the Einstein case at fixed horizon radius.
  • The electromagnetic Hawking power is suppressed by a factor of roughly 10^{-5}.
  • Increasing the Lovelock order N shifts the electromagnetic Hawking radiation toward dominance by the scalar-type polarization.
  • Pure Lovelock black holes remain geometrically more transparent to test fields than their Einstein counterparts yet radiate far less overall.

Where Pith is reading between the lines

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

  • The temperature-driven suppression may lengthen the evaporation timescale for higher-dimensional black holes once higher-curvature terms are present.
  • The growing scalar-type dominance could serve as a potential observational signature distinguishing Lovelock gravity from Einstein gravity if extra dimensions are realized.
  • Similar temperature-versus-transmission competition could be checked in other higher-curvature theories by extending the same greybody integration methods.

Load-bearing premise

The test-field approximation on the fixed pure Lovelock background metric gives accurate greybody factors without important back-reaction or numerical-integration artifacts.

What would settle it

A direct numerical integration of the wave equations on the pure Lovelock metric that produces transmission probabilities low enough to make the total radiated power comparable to or larger than the Schwarzschild-Tangherlini case at the same horizon radius.

Figures

Figures reproduced from arXiv: 2605.09756 by Jayden Tan.

Figure 1
Figure 1. Figure 1: Effective scalar potentials for the pure Lovelock black hole with [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Greybody factors of the minimally coupled test scalar field for the pure Lovelock black [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reduced partial scalar absorption cross sections for the pure Lovelock black hole with [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the critical pure Lovelock sequence ( [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Benchmark comparison of pure Lovelock and Tangherlini scalar scattering in [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Benchmark electromagnetic scattering for the pure Lovelock black hole with [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Electromagnetic greybody comparisons. Left: lowest scalar-type and vector-type elec [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Electromagnetic Hawking emissivity. Left: scalar-type, vector-type and total benchmark [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

Pure Lovelock black holes are geometrically more transparent than their Einstein counterparts, but they radiate far less. We compute scalar and higher-dimensional electromagnetic greybody factors and Hawking spectra on the critical branch $d=2N+2$, compare them with Schwarzschild--Tangherlini black holes at the same horizon radius $r_h$, and show that the smaller Hawking temperature overwhelms the enhanced transmission. In the benchmark $d=6$ case, the integrated scalar and electromagnetic powers are reduced by about $10^{-3}$ and $10^{-5}$, respectively. We also find a clean higher-curvature signature: as the Lovelock order $N$ grows, Hawking radiation becomes increasingly dominated by the scalar-type electromagnetic sector.

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 paper computes greybody factors and Hawking spectra for test scalar and higher-dimensional electromagnetic fields on asymptotically flat pure Lovelock black holes in the critical branch d=2N+2. It compares the results to Schwarzschild-Tangherlini black holes at fixed horizon radius r_h, concluding that the lower Hawking temperature dominates over any transmission enhancement from the more transparent geometry, yielding integrated power reductions of order 10^{-3} (scalar) and 10^{-5} (EM) for the d=6 benchmark. It further identifies a higher-curvature signature in which the scalar-type electromagnetic sector increasingly dominates the radiation as the Lovelock order N grows.

Significance. If the numerical results are robust, the work establishes a concrete, falsifiable distinction between pure Lovelock and Einstein gravity in the Hawking radiation channel. The quantitative suppression factors and the N-dependent mode dominance provide a clean higher-curvature signature that could be relevant for understanding evaporation in higher-dimensional modified gravity. The direct comparison at fixed r_h isolates the effect of the Lovelock curvature terms without confounding changes in horizon size.

major comments (2)
  1. [§5] §5 (d=6 benchmark results): The central quantitative claims—that scalar and electromagnetic radiated powers are reduced by factors ∼10^{-3} and ∼10^{-5} relative to the Schwarzschild-Tangherlini case—rest on the numerical solution of the radial wave equations followed by integration against the Hawking spectrum. The manuscript must supply convergence tests for the ODE solver, the frequency cutoff and tail integration procedure, and explicit error estimates on the integrated powers; without these, it is impossible to confirm that temperature suppression truly overwhelms the enhanced transmission.
  2. [§6] §6 (N-dependence): The claim that Hawking radiation becomes increasingly dominated by the scalar-type electromagnetic sector as N increases is load-bearing for the higher-curvature signature. The paper should present explicit ratios or separate spectra for at least three values of N (e.g., N=2,3,4) together with the corresponding greybody factors to demonstrate the trend quantitatively rather than qualitatively.
minor comments (2)
  1. [Abstract] The abstract states the reductions as “about 10^{-3}” and “10^{-5}”; reporting the precise numerical values (or at least the number of significant figures) would improve reproducibility.
  2. [§3] Notation for the higher-dimensional electromagnetic field decomposition into scalar-type and vector-type sectors should be defined once in §3 or §4 and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive evaluation of its significance. The comments highlight important aspects of the numerical robustness and the quantitative presentation of the N-dependence. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§5] §5 (d=6 benchmark results): The central quantitative claims—that scalar and electromagnetic radiated powers are reduced by factors ∼10^{-3} and ∼10^{-5} relative to the Schwarzschild-Tangherlini case—rest on the numerical solution of the radial wave equations followed by integration against the Hawking spectrum. The manuscript must supply convergence tests for the ODE solver, the frequency cutoff and tail integration procedure, and explicit error estimates on the integrated powers; without these, it is impossible to confirm that temperature suppression truly overwhelms the enhanced transmission.

    Authors: We agree that convergence tests and error estimates are necessary to substantiate the numerical results. In the revised manuscript we will add a new subsection in §5 (and supporting material in the appendices) that reports: (i) convergence of the radial ODE solutions under variations of integration step size and asymptotic boundary conditions, (ii) stability of the integrated powers with respect to the frequency cutoff and the tail-integration cutoff, and (iii) explicit error bars on the reported suppression factors (10^{-3} for scalars and 10^{-5} for electromagnetism). These additions will confirm that the temperature suppression dominates the transmission enhancement within the quoted precision. revision: yes

  2. Referee: [§6] §6 (N-dependence): The claim that Hawking radiation becomes increasingly dominated by the scalar-type electromagnetic sector as N increases is load-bearing for the higher-curvature signature. The paper should present explicit ratios or separate spectra for at least three values of N (e.g., N=2,3,4) together with the corresponding greybody factors to demonstrate the trend quantitatively rather than qualitatively.

    Authors: We accept that a quantitative demonstration for several values of N strengthens the higher-curvature signature. In the revision we will extend the analysis to N=2, 3 and 4. For each N we will present: separate Hawking spectra for the scalar and electromagnetic sectors, the associated greybody factors, and explicit ratios of the scalar-type to vector-type electromagnetic contributions. These results will be collected in an updated §6 together with a new figure and a summary table that makes the N-dependent dominance trend fully quantitative. revision: yes

Circularity Check

0 steps flagged

No circularity: direct numerical evaluation of greybody factors on fixed metric

full rationale

The paper computes greybody factors by solving the radial wave equations for test scalar and electromagnetic fields on the given pure Lovelock metric (critical branch d=2N+2), then integrates the transmission probabilities |T(ω)|^2 against the Hawking spectrum to obtain the radiated power. These steps are standard first-principles calculations in curved-spacetime QFT with no fitted parameters, no self-definitional relations, and no load-bearing self-citations that reduce the results to the inputs by construction. The comparison to Schwarzschild-Tangherlini at fixed r_h and the reported reductions (∼10^{-3} scalar, ∼10^{-5} EM for d=6) follow directly from the numerical integration without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard test-field approximation and the pure Lovelock metric in the critical branch; no additional free parameters or new postulated entities are introduced.

axioms (2)
  • domain assumption The background is the asymptotically flat pure Lovelock black hole on the critical branch d=2N+2.
    Defines the fixed geometry used to derive the wave equations.
  • domain assumption Scalar and electromagnetic test fields propagate linearly on this fixed background.
    Standard approximation allowing greybody factors to be computed from the wave equation alone.

pith-pipeline@v0.9.0 · 5419 in / 1448 out tokens · 82690 ms · 2026-05-12T02:17:38.330020+00:00 · methodology

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Reference graph

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