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Regular Rotating Black Hole: Probing the boundaries of the Radiative Signatures and Jet Power

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read The paper claims that jet-power and radiative-efficiency data from six Galactic X-ray binaries bound the MOG regular black hole deviation parameter to beta below about 0.4, and that GRS 1915+105 is left with no common parameter space.

desk verdict First combined radiative-efficiency + BZ jet-power constraints for regular rotating MOG black holes, but the bounds are conditional on Kerr-calibrated spins and a Kerr-fitted jet-power normalization; the GRS 1915+105 tension is the one result that probably survives. read the letter →

arxiv 2508.03473 v1 pith:NZC74YK2 submitted 2025-08-05 astro-ph.HE gr-qc

classification astro-ph.HEgr-qc
keywords regularblackholesMOGgravityscalar-tensor-vectorBlandford-ZnajekjetsradiativeefficiencyholespinX-raybinariesGRS1915+105
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to test whether a regular rotating black hole in scalar-tensor-vector gravity, one whose interior is nonsingular, can reproduce what is observed from six Galactic X-ray binaries. It claims that when the measured radiative efficiency and the Blandford-Znajek jet power are required to hold simultaneously, the deviation parameter $\beta$ of the regular geometry is bounded above by about 0.4 for most sources. For the rapidly spinning source GRS 1915+105 the bound is much tighter, and at the Kerr-inferred spin no point in the $(\beta,a)$ plane fits both observables. This matters because it turns a free parameter of a proposed modified-gravity black hole into an observationally measured quantity, and because it identifies near-extremal spins as the regime where the model becomes falsifiable.

What carries the argument

The argument runs through three linked pieces: the regular rotating MOG metric obtained by a modified Newman-Janis procedure, the Novikov-Thorne radiative efficiency set by the innermost stable circular orbit, and a Blandford-Znajek jet-power calculation carried out in horizon-regular Kerr-Schild coordinates. The new object is the regularization factor $\xi = 1 - F(r_H)$, which multiplies the jet power as $P = \frac{1}{6\pi}\,\xi\,\Phi_{\mathrm{tot}}^2\,\Omega_H^2$, where $\Omega_H$ is the horizon angular frequency. Because both $\Omega_H$ and the ISCO radius depend on $\beta$ and the spin $a$, the overlapping allowed regions in the $(\beta,a)$ plane from the two observables carry the constraint.

What would settle it

Fit GRS 1915+105's thermal continuum and reflection spectrum directly with the regular MOG metric rather than the Kerr metric, and recalibrate the Blandford-Znajek normalization $K$ inside that metric. If a solution with $\beta > 0.08$ simultaneously reproduces the observed radiative efficiency and jet power within errors, the paper's central exclusion is refuted.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is that the same geometry cannot freely explain both how efficiently matter radiates while spiraling into the hole and how much power the Blandford-Znajek mechanism extracts from the horizon. For the five systems with moderate spins the intersection of the two constraints forces the deviation parameter below about $\beta \simeq 0.4$, close to the horizonless threshold $\beta_c \simeq 0.402$. For GRS 1915+105, whose continuum-fitting spin exceeds 0.98, the efficiency contour alone limits $\beta$ to roughly 0.08, and there is no point in the allowed horizon region that simultaneously reproduces the measured jet power and the measured efficiency. The paper also derives a modified jet-power formula for regular black holes, in which the regularization factor $1 - F(r_H)$ multiplies the usual $\Omega_H^2$ dependence.

Load-bearing premise

The load-bearing premise is that continuum-fitting spins, Novikov-Thorne efficiencies, and the jet-power normalization $K$ measured under the Kerr metric remain unchanged when the spacetime is replaced by the regular MOG metric; if those calibrations must be redone from scratch in the new geometry, the $\beta$ bounds drawn from the overlap regions do not follow.

Editorial extensions

If this is right

  • For the five lower-spin binaries, requiring jet power and radiative efficiency simultaneously forces $\beta \lesssim 0.4$, so the horizonless part of the MOG parameter space ($\beta > \beta_c$) is excluded by these data.
  • GRS 1915+105, with a continuum-fitting spin above 0.98, cannot be described by the regular MOG black hole with both jet power and efficiency matched, so either its Kerr-based spin estimate or the model itself has to give.
  • Regular black holes do not inherit the Kerr Blandford-Znajek scaling unchanged: the factor $1 - F(r_H)$ suppresses jet power at fixed spin, so high observed jet power cannot be read directly as high spin in this geometry.
  • The method of overlapping jet-power and efficiency regions gives a reusable diagnostic for confronting other non-Kerr geometries with electromagnetic observations of accreting black holes.

Reading between the lines

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

  • Editorial inference: if the $\beta \lesssim 0.4$ bound holds, spin values routinely quoted for stellar-mass black holes under the Kerr assumption cannot simply be transplanted into regular MOG models; the high-spin tail becomes the sharpest discriminator between the two geometries.
  • Editorial inference: the same two-observable overlap test can be applied to other regular metrics, such as Bardeen, Hayward, or loop-quantum-corrected holes, replacing $F(r)$ in the jet-power formula; their survival against these data would follow from the same plots.
  • Editorial inference: an independent measurement of horizon angular frequency, for example through future gravitational-wave ringdown observations of a comparable-mass merger, could test the $\Omega_H^2$ dependence of the jet-power formula without relying on efficiency assumptions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies regular rotating black holes in scalar-tensor-vector gravity (MOG), parametrized by a deviation parameter β in addition to spin a. It computes the ISCO radius, Novikov-Thorne radiative efficiency η_NT(a,β), and Blandford-Znajek jet power including a 'regularization factor' 1−F(r_H). These theoretical predictions are then compared with observed radiative efficiencies and radio jet powers of six Galactic X-ray binaries (A0620-00, H1743-322, XTE J1550-564, GRS 1124-683, GRO J1655-40, GRS 1915+105). The central results are stated in Section 5: most sources allow β ≲ 0.38–0.4, the near-extremal source GRS 1915+105 requires β ≲ 0.08, and for GRS 1915+105 no simultaneous parameter space can explain both the radiative efficiency and the jet power. The paper also presents a modified Newman-Janis procedure for generating rotating regular solutions and an analytic BZ jet-power formula.

Significance. The paper's theoretical machinery is a useful contribution: the ISCO/efficiency and jet-power derivations are explicitly presented, internally consistent, and reduce to the Kerr results in the β→0 limit, and the regularization factor in Eq. (68) is a clear new element of the BZ formula. If the constraints were model-independent, the exclusion of large β for near-extremal sources and the apparent tension for GRS 1915+105 would be interesting observational tests of regular black holes and MOG. However, both observational arms of the comparison import quantities that are calibrated under the Kerr metric, so the headline β bounds are conditional on deviations from Kerr being small. The paper therefore currently offers a promising consistency-check framework rather than a fully model-independent constraint.

major comments (3)
  1. [Section 4, Table 2, Eq. (32)] The radiative-efficiency arm equates the MOG-theory efficiency η_NT(a,β) with the observed efficiencies listed in Table 2, but the table explicitly states that those spins and efficiencies are 'calculated under the assumption of the Kerr metric.' A continuum-fitting spin is not a spacetime-independent observable: it is inferred using the Kerr ISCO, so the same spectral data analyzed in the MOG metric would in general yield a different spin and a different efficiency. The blue regions in Figs. 6–11 therefore show where MOG reproduces a Kerr-derived quantity, not where MOG reproduces the observed spectrum. The β bounds and the claimed no-overlap for GRS 1915+105 depend on this re-interpretation. A concrete fix would be to forward-model the thermal continuum in the MOG metric for at least GRS 1915+105 and one lower-spin source, or to explicitly reframe all constraints as conditional consistency checks and soften the abstract and conclusion accordingly.
  2. [Section 4, Eqs. (36)–(37)] The jet-power arm imports the normalization log K = 2.94 ± 0.22 (Γ = 2) and log K = 4.19 ± 0.22 (Γ = 5) from ref. [73], which are fits to jet powers under the Kerr metric, with the stated assumption that 'K is independent of the spacetime geometry.' This assumption is load-bearing: K encodes Φ_tot² and the field-line angular-velocity distribution, both of which can depend on the near-horizon geometry. A shift in log K comparable to its quoted uncertainty would move the green regions in Figs. 6–11 substantially, and the claimed absence of an overlap region for GRS 1915+105 depends on this calibration. The authors should quantify this systematic uncertainty or provide a physical argument for why K is universal across Kerr and MOG spacetimes before presenting the bounds as observational constraints on β.
  3. [Section 5, Eq. (19), Fig. 1] The headline bound β ≲ 0.38–0.4 for most sources is only slightly below the theoretical horizon cap β_c ≈ 0.402 derived in Eq. (19). For five of the six sources the observational analysis excludes only a narrow strip of parameter space that is already nearly excluded by the existence of a horizon, so the claim of 'stringent observational bounds' in the abstract is supported mainly by GRS 1915+105. The paper should quantify how much of the allowed β range is excluded by data versus by the horizon condition, and should distinguish the weak typical constraint from the strong GRS 1915+105 constraint in the summary of results.
minor comments (5)
  1. [Appendix A.2.2, Eq. (25a)] Equation (25a) uses f(r,θ), but f was defined as f(r) in Eq. (21b); please define f(r,θ) explicitly and check the Kerr limit of the displayed coordinate transformation, which as written does not reduce to the usual Kerr-Schild shift combination.
  2. [Fig. 7 caption] The caption refers to 'T ab. 2' for the jet-power values, but the jet powers are listed in Table 3; please correct the cross-reference.
  3. [Section 4.1.1, Table 2] For A0620-00 the text reports a 90% spin range −0.59 < a < 0.49 while Table 2 lists a = 0.12 ± 0.19; please clarify which range is used for the efficiency error bars and how the asymmetric errors in Table 2 are propagated into the blue regions.
  4. [Abstract and Section 4] The abstract states that the analysis uses 'updated measurements from continuum fitting and Fe-line methods,' but the constraints in Section 4 are based on continuum-fitting spins for all sources; the Fe-line values are mentioned only in the text for XTE J1550-564 and GRO J1655-40. Please reconcile this wording.
  5. [Appendix A.1] The abstract and Section 5 describe the rotating-solution construction as a 'modified method,' but the procedure presented is the Azreg-Aïnou method of ref. [50] applied to a known static solution; the novelty should be stated more modestly or the differences should be made explicit.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the beta constraints are intersections of MOG model curves with externally adopted (Kerr-calibrated) observables, not fits renamed as predictions.

full rationale

The paper's central derivation is self-contained: the ISCO radius, radiative efficiency, horizon angular velocity, and Blandford-Znajek jet power are all computed from the explicit MOG metric functions given in Eqs. (16), (20)-(24), (32), and (68), with the regularization factor xi = 1 - F(rH) appearing in the jet power formula. The observational inputs are treated as external: spins and efficiencies are taken from the literature (Table 2), and the jet-power normalization K is imported from the independent calibration in reference [73]. The paper explicitly discloses that these inputs are Kerr-derived ('calculated under the assumption of the Kerr metric' and 'Assuming K is independent of the spacetime geometry'), which makes the resulting beta bounds conditional on those calibration choices. However, this is a model-dependence limitation, not a circular reduction by construction: the blue and green regions in Figs. 6-11 are obtained by solving the model equations for parameter combinations that reproduce the adopted observables, and beta=0 is not imposed as an identity but is merely one boundary of the allowed region. Moreover, the common beta ≲ 0.4 bound for most sources is dominated by the theory's own horizon cap beta_c = 0.402186 (Eq. 19), which is derived within the paper, rather than by a fitted parameter. The GRS 1915+105 bound (beta ≲ 0.08) reflects a genuine high-efficiency, high-spin tension. Because the paper neither fits beta to the same quantity it later predicts nor relies on a load-bearing chain of self-citations, no significant circularity is found.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a chain of imported ingredients: the MOG action and static regular solution from earlier work, the Azreg-Ainou rotation procedure, the Novikov-Thorne disk model, the BZ split-monopole magnetosphere, and Kerr-calibrated observational values for eta and K. The paper's own contribution is to combine these and add the regularization factor xi to the jet power. No new entities are invented, but several load-bearing assumptions are inherited.

free parameters (3)
  • K, magnetic flux normalization = log K = 2.94 ± 0.22 (Gamma=2) and 4.19 ± 0.22 (Gamma=5)
    Taken from the Kerr-based fit in reference [73] and assumed unchanged for MOG. The jet-power constraint is log P = log K + log[1-F(r_H)] + 2 log Omega_H, so the beta bounds scale directly with K.
  • Jet Lorentz factor Gamma = 2 and 5
    Chosen by hand as the lower and upper ends of the expected range; the Doppler-corrected jet powers differ by more than an order of magnitude between the two choices.
  • Jet-power uncertainty = 0.3 dex
    Assumed uniformly for every source to draw the green bands; no propagated distance, mass, or inclination errors enter the jet-power comparison.
assumptions (7)
  • domain assumption MOG/STVG reduces to Einstein gravity plus a massless Proca vector field near compact objects
    Section 2.1 assumptions (a)-(c); this effective action is the basis of the static solution and everything that follows.
  • domain assumption The static regular MOG spacetime F(r) in Eq. (16) is the correct seed for rotation
    Imported from [35]; the paper does not re-derive the solution from the STVG field equations.
  • standard math The Azreg-Ainou non-complexification method with Psi = r^2 + a^2 cos^2 theta produces a valid rotating MOG metric
    Appendix A.1, Eq. (44); the paper asserts that the Einstein tensor has the rotating imperfect-fluid form but does not show the explicit calculation.
  • domain assumption Novikov-Thorne disk with ISCO as inner edge describes the observed disk emission
    Section 3.1; all radiative efficiency constraints depend on this disk model.
  • domain assumption Blandford-Znajek split-monopole magnetosphere with field line angular velocity omega = Omega_H/2
    Appendix A.2, Eqs. (63)-(67); the power formula uses the energy-extremizing choice for omega and a monopolar flux profile.
  • ad hoc to paper The Kerr-calibrated normalization K is independent of spacetime geometry and universal across sources
    Section 4 states 'Assuming K is independent of the spacetime geometry'. Without this, the jet-power curves in Figs. 6-11 shift.
  • ad hoc to paper Radiative efficiencies listed in Table 2, computed from Kerr spin measurements, can be applied to MOG without re-fitting
    The eta values are derived under the Kerr metric; using them to constrain beta assumes they are metric-independent observables.

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Pith. "Pith review of Regular Rotating Black Hole: Probing the boundaries of the Radiative Signatures and Jet Power." pith.science (2026). https://pith.science/paper/NZC74YK2

@misc{pith2026250803473,
  author       = {Pith},
  title        = {Pith review of: Regular Rotating Black Hole: Probing the boundaries of the Radiative Signatures and Jet Power},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NZC74YK2}},
  note         = {Machine review of arXiv:2508.03473}
}
abstract

We perform a detailed observational analysis of several galactic X-ray binaries, focusing on the interplay between black hole spin, jet power, and radiative efficiency within the context of Blandford-Znajek-powered jets. Using updated measurements from continuum fitting and Fe-line methods, we constrain the spin parameter a and the deviation parameter $\beta$ for five key black hole systems: H1743-322, XTE J1550-564, GRS 1124-683, GRO J1655-40, and GRS 1915+105. For each system, we compare the allowed parameter spaces derived independently from observed radiative efficiencies and emitted jet powers under different assumptions for the jet Lorentz factor $\Gamma=2,5$. By overlapping these observational constraints with theoretical expectations for regular black holes, we assess the viability of various spin-deviation combinations in explaining the observed phenomena. Our results reveal significant restrictions on the allowed values of $\beta$, with typical upper bounds around 0.38 - 0.4, except for rapidly spinning sources where the constraint becomes notably tighter. We further present a modified method for generating rotating solutions from static regular black hole spacetimes and provide a robust theoretical framework for relating jet power to black hole angular frequency in curved geometries. We also find that the theoretical jet power is modified by regularization factor for regular black holes. These findings place stringent observational bounds on deviations from the Kerr geometry and provide important insight into the astrophysical mechanisms powering accreting stellar-mass black holes.

Figures

Figures reproduced from arXiv: 2508.03473 by the authors.

Figure 1
Figure 1. The parameter space for the existence of horizon ha [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. The variation of angular velocity of horizon [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Variation of the radius of Innermost Stable Circular Orbit (rISCO) has been depicted with the variation of the dimensionless characteristic parameter β and spin parameter a of the black hole. Both prograde and retrograde orbits have been considered in the analysis. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: The change in radiative efficiency ηNT has been depicted with the variation of the spin parameter a of the black hole for a set of different values of dimensionless characteristic parameter β. Maximum efficiency can be obtained for the prograde motion of the particle. …
Figure 5
Figure 5. Figure 5: The maximum efficiencies of regular Kerr-MOG black hole for various values of dimensionless parameter β have been displayed with the green dots. The green solid line and dashed blue line joining the dots has been produced by fitting polynomial of order 6 and 3, respect…
Figure 6
Figure 6. Figure 6: Constraints on the spin parameter a and the MOG parameter β for the black hole candidate A0620–00 has been shown. The blue shaded region corresponds to parameter values that yield a radiative efficiency consistent with the observed value ηNT = 0.061+0.009 −0.007. The g…
Figure 7
Figure 7. Figure 7: Jet power and radiative efficiency constraints for the black hole system H1743–322 are illustrated. In each panel, the green shaded region indicates the combinations of the MOG parameter β and spin a that successfully reproduce the observed jet power, accounting for un…
Figure 8
Figure 8. Figure 8: Parameter constraints for the black hole binary XTE J1550−564 are presented. The green shaded regions in panels (a) and (b) depict the combinations of the MOG parameter β and spin a that yield theoretical jet power in agreement with the observed radio luminosity, after…
Figure 9
Figure 9. Figure 9: Parameter space analysis for the black hole candidate GRS 1124−683 has been performed. Panel (a) demonstrates that for a jet Lorentz factor Γ = 2, there exists narrow region in the (a, β) parameter space that simultaneously accounts for both the observed jet power and …
Figure 10
Figure 10. Figure 10: Parameter constraints for GRO J1655−40 have been depicted. The ’panel(a)’ and ’panel (b)’ correspond to Lorentz factors Γ = 2 and Γ = 5, respectively. In both cases, regular rotating black hole in MOG theory provides a consistent description of the observed radiative …
Figure 11
Figure 11. Figure 11: Analysis of the black hole candidate GRS 1915+105 is presented. Panels (a) and (b) indicate that within the framework of a regular rotating spacetime in MOG theory of gravity, it remains challenging to simulta￾neously reproduce both the observed jet power and the meas…
Figure 12
Figure 12. Figure 12: Geometric representation of the poloidal [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]

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