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Blandford-Znajek Scaling in a Power-Law Rotating Kalb-Ramond Geometry: Magnetic-Flux Systematics and Bayesian Identifiability

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Within an adopted power-law rotating Kalb-Ramond background, the Blandford-Znajek jet-power proxies from two microquasars do not independently determine the deformation: the posterior tracks the effective prior and the jet-only profile is…

desk verdict Honest identifiability null: jet-power proxies don't pin down the KR hair in this adopted geometry, but the physical interpretation rests on an unverified rotating metric. read the letter →

arxiv 2608.11962 v1 pith:UKMCXFXK submitted 2026-08-12 gr-qc

Sardor Murodov , Olimjon Kholturayev , Bekzod Rahmatov , Javlon Rayimbaev , Islom Egamberdiev , Shavkat Karshiboev This is my paper · ORCID
classification gr-qc PACS 04.70.-s95.30.Sf
keywords Blandford-ZnajekmechanismKalb-Ramondgravityblackholejetsnon-KerrmetricBayesianidentifiabilitymagneticfluxprescriptionmicroquasarjetpowersLorentzviolation
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 asks whether relativistic jet power, through the Blandford–Znajek mechanism, can measure the Lorentz-violating Kalb–Ramond deformation of a rotating black hole. Working with an adopted power-law rotating Kalb–Ramond metric, it finds the answer is no: for two well-studied microquasars, the inferred deformation posterior tracks the horizon-conditioned effective prior ($R_{68}=0.990$, median shift $S_\Gamma\simeq -0.11$), and the jet-only profile likelihood varies by only about $1.4\times10^{-2}$ across the allowed range. The result matters because jets are often proposed as strong-field probes of gravity; if this conclusion holds, any jet-power constraint on such geometries must be read as a compatibility region shaped by priors and magnetic-flux assumptions rather than as a measurement of the deformation. The paper also shows that the magnetic-flux prescription is itself a leading systematic and that the $s=2$ member of the metric family is exactly Kerr after a mass redefinition.

What carries the argument

The argument rides on three pieces. The first is the adopted rotating metric Eq. (10), whose horizon equation is $\Delta_{KR}=r^2-2Mr+a^2+\Gamma r^n=0$ with $n=2(s-1)/s$; the horizon radius $r_H$ is its largest root and the horizon angular velocity is $\Omega_H^{KR}=a/(r_H^2+a^2)$. The second is the leading Blandford–Znajek power formula $P_{BZ}\propto\Phi_H^2\Omega_H^2 x(1-x)$ with $x=\Omega_F/\Omega_H$, evaluated at impedance matching $x=1/2$, together with three magnetic-flux prescriptions: fixed total flux $\Phi_H$, fixed local normal field $B_H$ with proper flux $\Phi_H\simeq 2\pi B_H(r_H^2+a^2)$, and the reduced proxy $\Phi_{\rm proxy}\propto r_H^2$. The third is the Bayesian identifiability test, which compares the posterior of the dimensionless amplitude $\bar\Gamma$ with the horizon-conditioned effective prior and computes a jet-only profile chi-square $\chi^2_{\rm prof}(\bar\Gamma)$ with nuisance parameters profiled out.

What would settle it

Run a global force-free or GRMHD simulation in this rotating Kalb-Ramond geometry with a source-calibrated horizon flux and recompute the jet-only profile chi-square over the allowed $\bar\Gamma$ range; if the maximum variation exceeds $\Delta\chi^2\simeq 1$, the jet data would identify the deformation and the flatness result would be refuted, whereas a flat profile would confirm it.

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Extended reading notes

Core claim

The central claim is that, in the adopted power-law rotating Kalb–Ramond geometry, the leading Blandford–Znajek jet power does not independently determine the Kalb–Ramond hair amplitude $\Gamma$. At the metric level the $s=2$ slice collapses into Kerr under the mass redefinition $M_{\rm eff}=M-\Gamma/2$, and for $s>2$ the deformation decays more slowly than the mass term, so the paper uses $s=3/2$ as the primary benchmark. Across three magnetic prescriptions—fixed total horizon flux, fixed local normal field with proper horizon area, and a radius-based flux proxy—the jet-power trends differ appreciably. For the two microquasar jet proxies, the marginalized posterior for $\Gamma$ closely follows the horizon-conditioned effective prior under both a uniform and a truncated-Gaussian deformation prior, with $R_{68}=0.990$ and $S_\Gamma\simeq -0.11$ in both runs, and the jet-only profile chi-square varies by only $\sim 1.4\times10^{-2}$ over the full allowed interval. The paper concludes that these posterior intervals are compatibility regions shaped by the prior structure, the horizon-existence boundary, the common normalization, and intrinsic scatter, not independent jet-driven measurements of $\Gamma$.

Load-bearing premise

The load-bearing premise is that the adopted rotating metric is a real stationary spacetime, yet the paper does not verify that the metric together with a rotating Kalb-Ramond two-form satisfies the complete Einstein–Kalb–Ramond field equations.

Editorial extensions

If this is right

  • Any jet-power constraint on this Kalb-Ramond geometry must specify which magnetic quantity is held fixed, because fixed total flux, fixed local field, and the radius proxy give opposite or vanishing leading trends.
  • An apparent detection of the hair at $s=2$ would be a mass reparameterization rather than a non-Kerr effect, since that slice is exactly Kerr with $M_{\rm eff}=M-\Gamma/2$.
  • The $s=3/2$ and $s=3$ benchmarks both show prior-shaped posteriors and near-flat jet-only profiles, so the weak identifiability is not an artifact of the chosen radial exponent.
  • A genuine jet-based bound would require a self-consistent rotating Kalb-Ramond background with controlled asymptotics, source-dependent or hierarchical magnetic-flux modeling, non-Kerr spin inference, a larger source sample, and a global force-free or GRMHD magnetospheric calculation.

Reading between the lines

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

  • If this non-identifiability generalizes, jet-power bounds on non-Kerr parameters in other modified-gravity metrics may likewise be prior-dominated; rerunning the effective-prior and profile-likelihood diagnostics on those analyses would settle that.
  • Because the fixed-local-field prescription cancels the explicit horizon-radius dependence at leading order, any future detection of the Kalb-Ramond deformation through BZ power would have to come from global magnetospheric effects—field geometry, flux saturation, or the coefficient $\kappa_{BZ}$—rather than from horizon geometry alone.
  • The same two-diagnostic test could be run on a larger microquasar sample or on AGN jet data with source-specific flux estimates; a profile that stays flat in $\bar\Gamma$ would confirm the non-identifiability, while a profile rising above $\Delta\chi^2\approx 1$ would overturn it.
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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

2 major / 4 minor

Summary. This paper studies the leading Blandford–Znajek jet-power scaling in the four-dimensional power-law rotating Kalb–Ramond metric of Kumar, Ghosh, and Wang. It shows that the s=2 member reduces exactly to Kerr after a mass redefinition, selects the nondegenerate s=3/2 case as the primary benchmark, compares three magnetic-flux prescriptions (fixed total horizon flux, fixed local normal field with proper area, and a coordinate-radius proxy), and then performs a two-source Bayesian consistency test using GRO J1655–40 and GRS 1915+105. The central result is that the marginalized posterior for the hair amplitude closely tracks the horizon-conditioned effective prior (R68≈0.990 in both runs, SΓ≈−0.11), and the jet-only profile chi-square varies by only about 1.4×10^-2 across the allowed range. The paper concludes that, within the adopted setup, the jet-power proxies do not independently determine the Kalb–Ramond deformation, and it explicitly scopes the analysis to the adopted stationary background rather than to a newly established exact rotating solution of the Einstein–Kalb–Ramond system.

Significance. If the adopted metric is accepted as a test-bed geometry, the paper is a well-executed identifiability and systematics study. It correctly identifies the s=2 metric degeneracy, demonstrates that the magnetic-flux prescription is a leading systematic, and cleanly separates posterior localization from likelihood information through effective-prior comparisons and a prior-independent profile diagnostic. The MCMC convergence diagnostics and the explicit Kerr limits are strengths, and the authors are unusually candid about the limitations of their setup. The main limitation is physical rather than statistical: because the rotating metric (10) is not verified as a solution of the complete Einstein–Kalb–Ramond field equations, the quantitative results establish a property of an adopted metric family, not of Kalb–Ramond gravity itself. This conditional character is stated in Sections II and VIII, but it remains the load-bearing connection between the otherwise sound identifiability analysis and the paper's advertised physical setting.

major comments (2)
  1. [Sec. II, Eq. (10); Sec. VIII] The adopted rotating metric is not checked against the complete Einstein–Kalb–Ramond field equations derived from Eq. (7). The paper explicitly says in Sec. II that it does not substitute the rotating metric and a rotating two-form back into the field equations, and Sec. VIII repeats that the spacetime is treated as an adopted stationary background. Because the horizon radius, horizon angular velocity, flux definitions, and all posterior results depend directly on Eq. (10), the central claim is conditional on an unverified background. The authors should either verify that Eq. (10), together with a rotating B_mu_nu, solves the field equations, or explicitly reframe the analysis as a phenomenological non-Kerr test and remove the claim that it constrains the Kalb–Ramond deformation. As written, the title and abstract invite a Kalb–Ramond-gravity interpretation that the paper itself disclaims.
  2. [Sec. VI.A, Eq. (108)] The truncated-Gaussian sensitivity prior is data-informed: the values mu_Gamma=-0.0144 and sigma_Gamma=0.0543 are the mean and standard deviation of viable points 'from a preliminary broad scan over the same top-hat spin supports after requiring a horizon and chi2_jet < 1.' Because the chi2_jet condition uses the jet data, the Gaussian prior is not a genuinely independent prior, and the comparison between the resulting posterior and the effective prior (which omits the jet likelihood) is partially circular. The uniform-prior run is clean and already supports the paper's qualitative conclusion, but Table III and Sec. VIII present both runs on equal footing. Please either use a prior constructed without any data-dependent cut, or clearly relabel the Gaussian run as a post-data sensitivity diagnostic rather than as a controlled prior test.
minor comments (4)
  1. [Figs. 2, 3, 5] The figure legends omit minus signs for negative values of the hair amplitude: e.g., 'bar_Gamma = 0.1' and '0.05' should read 'bar_Gamma = -0.1' and '-0.05' to match Eq. (93).
  2. [Sec. VI.C] The sentence beginning 'The results are Both width ratios...' is grammatically broken; it should read 'Both width ratios are within about one percent of unity, and both normalized median shifts are close to one tenth of an effective-prior standard deviation.'
  3. [Sec. VI.C, Eq. (115)] The denominator sigma_Gamma^prior is used before it is defined; please state explicitly that it is the standard deviation of the horizon-conditioned effective prior for the corresponding run.
  4. [Sec. VI.A] The spin priors in Table I are derived from Kerr-based continuum-fitting analyses, as the paper acknowledges. The effective prior is therefore not a fully self-consistent non-Kerr prior; please add one sentence in the effective-prior discussion reminding the reader that the spin supports themselves are Kerr-calibrated.

Circularity Check

1 steps flagged · score 1.0 of 10

The central identifiability claim is a self-consistent null result; only the truncated-Gaussian sensitivity prior is mildly self-informing, and it is explicitly non-load-bearing.

  1. fitted input called prediction [Sec. VI.A, Eq. (108) and Sec. VI.C, Table III.]
    "These localization values are the mean and standard deviation of viable points from a preliminary broad scan over the same top-hat spin supports after requiring a horizon and χ2_jet < 1. They are used only as a controlled prior-sensitivity diagnostic and are not independent observational information."

    The localization values µΓ=−0.0144 and σΓ=0.0543 are computed from the same two-source data and model used in the later comparison, by selecting viable points with χ2_jet < 1. The truncated-Gaussian 'sensitivity' run then reports that the posterior closely follows the corresponding effective prior, with R68=0.990, but that agreement is partly by construction because the prior itself was centered on data-compatible points of the same likelihood. This is a mild self-informing prior, not an independent check. It is, however, explicitly labeled as a diagnostic, and the primary uniform-prior run plus the prior-free profile likelihood (max ∆χ2_prof ≃ 1.37×10−2) reach the same conclusion, so this element is not the load-bearing part of the paper's argument.

full rationale

The paper's main claim is a negative identifiability result, and the checks used to establish it are self-contained. The metric (10) is explicitly adopted from Kumar, Ghosh, and Wang [54] rather than rederived, with repeated disclaimers that no complete Einstein–Kalb–Ramond solution is being established; that is a scope limitation, not circular reasoning. The s=2 degeneracy is a direct algebraic reduction to Kerr via the mass redefinition Meff=M−Γ/2, which is a mathematical identity rather than a fitted prediction. The fixed-flux BZ power P_KR_BZ ∝ (Ω_KR_H)^2 is computed from the metric's horizon equation, and the fixed-local-field cancellation in Eq. (88) is an explicit algebraic cancellation. The Bayesian identifiability analysis correctly compares the posterior with a horizon-conditioned effective prior that omits the jet likelihood, and the flat profile chi-square is computed without σint, so the conclusion that the jet proxies add essentially no independent information on Γ rests on the uniform-prior run and the profile diagnostic, both of which are prior-independent. The only mildly circular element is the truncated-Gaussian sensitivity prior, whose mean and width are derived from the same data/model; because the paper labels it as a diagnostic and the independent diagnostics agree, it raises the circularity score only marginally. The paper also explicitly flags the unverified rotating background, missing magnetospheric solution, and non-Kerr spin inconsistency as limitations, which further supports a low circularity score rather than a high one.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on an adopted, unverified rotating metric, on the standard leading-order BZ factorization, and on a deliberately simple two-source Bayesian model with a common normalization and scatter. The free parameters are the deformation amplitude, the normalization, the intrinsic scatter, the spin priors, and the hand-chosen radial exponent; the truncated-Gaussian prior parameters are data-informed. No new particles, forces, or conserved quantities are introduced.

free parameters (6)
  • Gamma_bar (dimensionless KR hair amplitude) = -0.029 +0.056/-0.049 (posterior median/credible interval, uniform prior)
    Target deformation parameter in the Bayesian model; it is sampled and the posterior mostly reflects the effective prior, not the jet likelihood.
  • A = log10 K (common normalization) = 2.829 (posterior median)
    Absorbs unknown flux normalization, magnetic geometry coefficient, and radio-to-jet conversion; it can compensate for Gamma_bar shifts and contributes to the flat profile.
  • sigma_int (intrinsic scatter) = 0.321 (posterior median)
    Source-to-source scatter in the log jet-power model; sampled with a wide prior and absorbs discrepancies between the two data points.
  • Spin parameters a_* for GRO J1655-40 and GRS 1915+105 = 0.733 and 0.971 (posterior medians)
    Gaussian observational priors from continuum fitting; they are sampled and can trade off against Gamma_bar. The paper notes these are Kerr-based proxy priors, not self-consistent non-Kerr spins.
  • Radial exponent s = 3/2 primary, 3 secondary
    Chosen by hand: s=2 is degenerate, s>2 has slow falloff, so s=3/2 is the nondegenerate benchmark. The identifiability conclusion is also tested at s=3.
  • Truncated-Gaussian prior parameters mu_Gamma, sigma_Gamma = -0.0144, 0.0543
    Derived from a preliminary broad scan requiring chi2_jet<1 on the same two-source data and model; used as a sensitivity prior, not independent observational information.
assumptions (6)
  • domain assumption The standard factorized Blandford-Znajek scaling P ∝ Phi^2 Omega_F(Omega_H - Omega_F), with the impedance-matched ratio x=1/2, applies in the adopted KR geometry.
    The paper does not solve a KR-specific Grad-Shafranov or GRFFE problem; the BZ coefficient and x are treated as model inputs (Sec. III.E, Sec. IV.A).
  • domain assumption The adopted rotating metric, Eq. (10), is a valid stationary background whose horizons are given by Delta_KR=0.
    The metric is taken from Kumar, Ghosh, and Wang [54] without verifying that it, together with a rotating KR two-form, satisfies the complete Einstein-KR field equations (Sec. II).
  • domain assumption The parameter relation s=|b^2| xi_2 and the dimensional scaling [Gamma]=L^(2/s) inherited from the static KR seed are correct.
    Used to define the dimensionless amplitudes Gamma_bar and Gamma_3 in Sec. II.B; inherited from the cited KR literature.
  • domain assumption The two microquasar spin priors and jet-power proxies used in Table I are representative proxies for the true jet and spin quantities.
    Adopted from Refs. [35, 80-93]; the paper cautions that the spins come from Kerr-based spectral analyses and are used only as proxy priors.
  • ad hoc to paper A single common effective Gamma_bar and a common normalization K apply to both sources.
    This is a simplifying diagnostic assumption stated in Sec. VI.A; the paper explicitly warns it must not be interpreted as a universal bound on the KR coupling.
  • standard math Maxwell's equations and the force-free conditions in Sec. III are standard and apply to the assumed magnetosphere.
    The stationary, axisymmetric force-free framework is the usual Blandford-Znajek starting point from the cited literature.

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Cite this review

Pith. "Pith review of Blandford-Znajek Scaling in a Power-Law Rotating Kalb-Ramond Geometry: Magnetic-Flux Systematics and Bayesian Identifiability." pith.science (2026). https://pith.science/paper/UKMCXFXK

@misc{pith2026260811962,
  author       = {Pith},
  title        = {Pith review of: Blandford-Znajek Scaling in a Power-Law Rotating Kalb-Ramond Geometry: Magnetic-Flux Systematics and Bayesian Identifiability},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UKMCXFXK}},
  note         = {Machine review of arXiv:2608.11962}
}
abstract

Relativistic jets from spinning black holes offer a possible strong-field probe of gravity through the Blandford-Znajek mechanism. We study the leading jet-power scaling in the four-dimensional power-law rotating Kalb-Ramond geometry introduced by Kumar, Ghosh, and Wang. The metric is used here as a stationary background, without assuming that it constitutes a newly established exact rotating solution. We first examine the deformation at the metric level. For $s=2$ it is absorbed completely by a mass redefinition, whereas for $s>2$ the correction decays more slowly than the usual mass term. Our main benchmark is therefore the nondegenerate $s=3/2$ case, whose correction falls faster than the Kerr mass term; $s=3$ is kept as a secondary comparison. We evaluate the BZ scaling under three magnetic assumptions: fixed total horizon flux, fixed local normal field with the proper horizon area, and a reduced radius-based flux proxy. The resulting trends differ appreciably, showing that the magnetic prescription is itself a leading systematic. For GRO J1655-40 and GRS 1915+105, the marginalized deformation posterior remains close to the horizon-conditioned effective prior for both a uniform prior and a truncated-Gaussian alternative. The jet-only profile likelihood is also nearly flat over the allowed deformation range, with the same qualitative behavior in the $s=3$ test. Thus, within the present setup, the jet-power proxies do not independently determine the Kalb-Ramond deformation. A stronger inference will require better control of the rotating background, source-dependent magnetic flux, non-Kerr spin estimates, and a larger sample.

Figures

Figures reproduced from arXiv: 2608.11962 by the authors.

Figure 1
Figure 1. Horizon-admitting parameter space in the [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Dimensionless outer horizon radius RH = rH/M as a function of the spin parameter a∗ for different values of the dimensionless hair amplitude Γ¯. The curve with Γ = 0 ¯ corresponds to the Kerr limit. 0.2 0.4 0.6 0.8 1.0 a* 0.0 0.1 0.2 0.3 0.4 0.5 M KR H (a) = 0.1 = 0.05 = 0 = 0.02 = 0.04 0.100 0.075 0.050 0.025 0.000 0.025 0.050 0.075 0.100 0.1 0.2 0.3 0.4 0.5 M KR H (b) a* = 0.2 a* = 0.5 a* = 0.7 a* = 0.9 a* = 0.975… view at source ↗
Figure 3
Figure 3. Dimensionless horizon angular velocity MΩ KR H . Panel (a): dependence on the spin parameter a∗ for representative values of Γ¯. Panel (b): dependence on Γ¯ for selected fixed spins. Positive values of Γ¯ enhance the horizon angular velocity, while negative values suppress it [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Fixed-flux reduced Blandford–Znajek power [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Fixed-flux deviation of the rotating Kalb–Ramond BZ power from Kerr. Panel (a): [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Contour plot of the fixed-flux reduced BZ power [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Sensitivity of the leading BZ power ratio to the magnetic-flux prescription for [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Posterior projection for GRO J1655–40 under the fixed-flux baseline. The displayed quantities are [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Posterior projection for GRS 1915+105 under the fixed-flux baseline. The high-spin proxy prior strongly intersects [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Posterior predictive distributions for the logarithmic observed jet-power proxies in the fixed- [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Latent fixed-ΦH mean relation between the logarithmic jet-power proxy and spin. The solid curve is the posterior median and the shaded region is the 68% credible band of the mean relation after marginalizing over Γ¯ and the common normalization A. The directly labeled…
Figure 12
Figure 12. Figure 12: Controlled prior-sensitivity analysis for the common KR hair amplitude. The horizon-conditioned effective prior is [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]

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Works this paper leans on

96 extracted references · 72 canonical work pages

  1. [1]

    constraint

    Degenerates= 2slice and nondegenerate benchmark A metric-level identifiability check is essential before using the hair parameter observationally. Fors= 2, Eq. (13) givesn= 1, and the two combinations carrying the deformation reduce to 2Mr−Γr= 2M effr,(15) ∆KR =r 2−2M effr+a 2,(16) where Meff≡M− Γ 2.(17) Because every occurrence ofMandΓin Eq. (10) enters ...

  2. [2]

    R. P. Fender, Powerful jets from black hole x-ray binaries in low/hard x-ray states, Monthly Notices of the Royal Astro- nomical Society322, 31 (2001)

    2001

  3. [3]

    R. P. Fender, T. M. Belloni, and E. Gallo, Towards a unified model for black hole x-ray binary jets, Monthly Notices of the Royal Astronomical Society355, 1105 (2004)

    2004

  4. [4]

    I. F. Mirabel and L. F. Rodriguez, A superluminal source in the galaxy, Nature371, 46 (1994). 26

    1994

  5. [5]

    R. M. Hjellming and M. P. Rupen, Episodic ejection of relativistic jets by the x-ray transient gro j1655–40, Nature375, 464 (1995)

    1995

  6. [6]

    A. A. Zdziarski, A. J. Tetarenko, and M. Sikora, Jet parameters in the black-hole x-ray binary maxi j1820+070, The Astrophysical Journal925, 189 (2022)

    2022

  7. [7]

    Carotenuto, A

    F. Carotenuto, A. J. Tetarenko, S. Corbel,et al., Modelling the kinematics of the decelerating jets from the black hole x-ray binary maxi j1348–630, Monthly Notices of the Royal Astronomical Society511, 4826 (2022)

    2022

  8. [8]

    Akiyama,et al., First m87 event horizon telescope results

    Event Horizon Telescope Collaboration, K. Akiyama,et al., First m87 event horizon telescope results. i. the shadow of the supermassive black hole, The Astrophysical Journal Letters875, L1 (2019)

    2019

Show all 96 references
  1. [9]

    Akiyama,et al., First m87 event horizon telescope results

    Event Horizon Telescope Collaboration, K. Akiyama,et al., First m87 event horizon telescope results. v. physical origin of the asymmetric ring, The Astrophysical Journal Letters875, L5 (2019)

    2019

  2. [10]

    Akiyama,et al., First sagittarius a* event horizon telescope results

    Event Horizon Telescope Collaboration, K. Akiyama,et al., First sagittarius a* event horizon telescope results. i. the shadow of the supermassive black hole in the center of the milky way, The Astrophysical Journal Letters930, L12 (2022)

    2022

  3. [11]

    R. D. Blandford and R. L. Znajek, Electromagnetic extraction of energy from kerr black holes, Monthly Notices of the Royal Astronomical Society179, 433 (1977)

    1977

  4. [12]

    J. C. McKinney, Total and jet blandford–znajek power in the presence of an accretion disk, The Astrophysical Journal Letters630, L5 (2005)

    2005

  5. [13]

    Garofalo, The spin dependence of the blandford–znajek effect, The Astrophysical Journal699, 400 (2009)

    D. Garofalo, The spin dependence of the blandford–znajek effect, The Astrophysical Journal699, 400 (2009)

    2009

  6. [14]

    Tchekhovskoy, R

    A. Tchekhovskoy, R. Narayan, and J. C. McKinney, Black hole spin and the radio loud/quiet dichotomy of active galactic nuclei, The Astrophysical Journal711, 50 (2010)

    2010

  7. [15]

    Narayan, R

    R. Narayan, R. F. Penna, and A. Sadowski, General relativistic magnetohydrodynamic simulations of blandford–znajek jets and the membrane paradigm, Monthly Notices of the Royal Astronomical Society436, 3741 (2013)

    2013

  8. [16]

    R. F. Penna, Black hole meissner effect and blandford–znajek jets, Physical Review D89, 104057 (2014)

    2014

  9. [17]

    R. F. Penna, Black hole jet power from impedance matching, Physical Review D92, 084017 (2015)

    2015

  10. [18]

    S. S. Komissarov, Direct numerical simulations of the blandford–znajek effect, Monthly Notices of the Royal Astronomical Society326, L41 (2001)

    2001

  11. [19]

    J. C. McKinney, General relativistic force-free electrodynamics: a new code and applications to black hole magnetospheres, Monthly Notices of the Royal Astronomical Society367, 1797 (2006)

    2006

  12. [20]

    J. C. McKinney and R. Narayan, Disc-jet coupling in black hole accretion systems – ii. force-free electrodynamical models, Monthly Notices of the Royal Astronomical Society375, 531 (2007)

    2007

  13. [21]

    S. S. Komissarov and J. C. McKinney, The meissner effect and the blandford–znajek mechanism in conductive black hole magnetospheres, Monthly Notices of the Royal Astronomical Society Letters377, L49 (2007)

    2007

  14. [22]

    Pan and C

    Z. Pan and C. Yu, Fourth-order split monopole perturbation solutions to the blandford–znajek mechanism, Physical Review D91, 064067 (2015)

    2015

  15. [23]

    S. Noda, Y. Nambu, and T. Tsukamoto, Blandford–znajek process as alfvénic superradiance, Physical Review D101, 023003 (2020)

    2020

  16. [24]

    Koide and T

    S. Koide and T. Imamura, Analytical and numerical methods and test calculations of one-dimensional force-free magne- todynamics on arbitrary magnetic surfaces across horizons of spinning black holes, The Astrophysical Journal881, 91 (2019)

    2019

  17. [25]

    Lyutikov and J

    M. Lyutikov and J. C. McKinney, Slowly balding black holes, Physical Review D84, 084019 (2011)

    2011

  18. [26]

    Camilloni, O

    F. Camilloni, O. J. C. Dias, G. Grignani, T. Harmark, R. Oliveri, M. Orselli, A. Placidi, and J. E. Santos, Blandford– znajek monopole expansion revisited: novel non-analytic contributions to the power emission, Journal of Cosmology and Astroparticle Physics2022(07), 032

  19. [27]

    Tchekhovskoy, R

    A. Tchekhovskoy, R. Narayan, and J. C. McKinney, Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole, Monthly Notices of the Royal Astronomical Society Letters418, L79 (2011)

    2011

  20. [28]

    J. C. McKinney, A. Tchekhovskoy, and R. D. Blandford, General relativistic magnetohydrodynamic simulations of mag- netically choked accretion flows around black holes, Monthly Notices of the Royal Astronomical Society423, 3083 (2012)

    2012

  21. [29]

    C. J. White, J. M. Stone, and E. Quataert, A resolution study of magnetically arrested disks, The Astrophysical Journal 874, 168 (2019)

    2019

  22. [30]

    Tchekhovskoy, J

    A. Tchekhovskoy, J. C. McKinney, and J. Dexter, Transient jet formation and state transitions from large-scale magnetic reconnection in black hole accretion discs, Monthly Notices of the Royal Astronomical Society440, 2185 (2014)

    2014

  23. [31]

    M. J. Avara, J. C. McKinney, and C. S. Reynolds, Efficiency of thin magnetically arrested discs around black holes, Monthly Notices of the Royal Astronomical Society462, 636 (2016)

    2016

  24. [32]

    Parfrey, A

    K. Parfrey, A. Philippov, and B. Cerutti, First-principles plasma simulations of black-hole jet launching, Physical Review Letters122, 035101 (2019)

    2019

  25. [33]

    C. B. Singh, D. Garofalo, and E. M. de Gouveia Dal Pino, Magnetic reconnection and blandford–znajek process around rotating black holes, Monthly Notices of the Royal Astronomical Society478, 5404 (2018)

    2018

  26. [34]

    R. D. Blandford and D. G. Payne, Hydromagnetic flows from accretion discs and the production of radio jets, Monthly Notices of the Royal Astronomical Society199, 883 (1982)

    1982

  27. [35]

    M. V. Barkov and S. S. Komissarov, Stellar explosions powered by the blandford–znajek mechanism, Monthly Notices of the Royal Astronomical Society Letters385, L28 (2008)

    2008

  28. [36]

    G. Pei, S. Nampalliwar, C. Bambi, and M. J. Middleton, Blandford–znajek mechanism in black holes in alternative theories of gravity, The European Physical Journal C76, 534 (2016)

    2016

  29. [37]

    J. Dong, N. Patiño, and Y. Xie, Blandford–znajek process in quadratic gravity, Physical Review D105, 044008 (2022). 27

    2022

  30. [38]

    Camilloni, T

    F. Camilloni, T. Harmark, and M. Orselli, Blandford–znajek jets in modified gravity, Journal of Cosmology and Astropar- ticle Physics2024(01), 047

  31. [39]

    I. K. Dihingiaet al., Enhanced blandford–znajek jet in loop quantum black hole, Journal of Cosmology and Astroparticle Physics2024(05), 101

  32. [40]

    Banerjee, B

    I. Banerjee, B. Mandal, and S. SenGupta, Signatures of einstein–maxwell dilaton–axion gravity from the observed jet power and the radiative efficiency, Physical Review D103, 044046 (2021)

    2021

  33. [41]

    Kalb and P

    M. Kalb and P. Ramond, Classical direct interstring action, Physical Review D9, 2273 (1974)

    1974

  34. [42]

    V. A. Kostelecky and S. Samuel, Spontaneous breaking of lorentz symmetry in string theory, Physical Review D39, 683 (1989)

    1989

  35. [43]

    Colladay and V

    D. Colladay and V. A. Kostelecky, Cpt violation and the standard model, Physical Review D55, 6760 (1997)

    1997

  36. [44]

    Colladay and V

    D. Colladay and V. A. Kostelecky, Lorentz-violating extension of the standard model, Physical Review D58, 116002 (1998)

    1998

  37. [45]

    V. A. Kostelecky, Gravity, lorentz violation, and the standard model, Physical Review D69, 105009 (2004)

    2004

  38. [46]

    Altschul, Q

    B. Altschul, Q. G. Bailey, and V. A. Kostelecky, Lorentz violation with an antisymmetric tensor, Physical Review D81, 065028 (2010)

    2010

  39. [47]

    Lambiase, Lorentz invariance breakdown and constraints from big-bang nucleosynthesis, Physical Review D72, 087702 (2005)

    G. Lambiase, Lorentz invariance breakdown and constraints from big-bang nucleosynthesis, Physical Review D72, 087702 (2005)

    2005

  40. [48]

    A. Das, T. Paul, and S. SenGupta, Invisibility of antisymmetric tensor fields in the light of f(r) gravity, Physical Review D98, 104002 (2018)

    2018

  41. [49]

    N. E. Mavromatos, Theory overview of testing fundamental symmetries, Hyperfine Interactions228, 7 (2014)

    2014

  42. [50]

    de Cesare, N

    M. de Cesare, N. E. Mavromatos, and S. Sarkar, On the possibility of tree-level leptogenesis from kalb–ramond torsion background, The European Physical Journal C75, 514 (2015)

    2015

  43. [51]

    L. A. Lessa, J. E. G. Silva, and R. V. Maluf, Modified black hole solution with a background kalb–ramond field, The European Physical Journal C80, 335 (2020)

    2020

  44. [52]

    W. Liu, D. Wu, and J. Wang, Static neutral black holes in kalb–ramond gravity, Journal of Cosmology and Astroparticle Physics2024(09), 017

  45. [53]

    Duan, J.-Y

    Z.-Q. Duan, J.-Y. Zhao, and K. Yang, Electrically charged black holes in gravity with a background kalb–ramond field, The European Physical Journal C84, 798 (2024)

    2024

  46. [54]

    Liu, S.-P

    J.-Z. Liu, S.-P. Wu, and S.-W. Wei, Exact black hole solutions in gravity with a background kalb–ramond field, Journal of Cosmology and Astroparticle Physics2025(11), 056

  47. [55]

    Kumar, S

    R. Kumar, S. G. Ghosh, and A. Wang, Gravitational deflection of light and shadow cast by rotating kalb–ramond black holes, Physical Review D101, 104001 (2020)

    2020

  48. [56]

    W. Liu, D. Wu, and J. Wang, Shadow of slowly rotating kalb–ramond black holes, Journal of Cosmology and Astroparticle Physics2025(05), 017

  49. [57]

    A. A. Araújo Filho, Particle creation and evaporation in kalb–ramond gravity, Journal of Cosmology and Astroparticle Physics2025(04), 076

  50. [58]

    A. A. Araújo Filho, Particle motion and thermal effects around a Kalb–Ramond black hole, The European Physical Journal C85, 1002 (2025), arXiv:2504.19246

    2025

  51. [59]

    Shi and A

    Y. Shi and A. A. Araújo Filho, Influence of a Kalb–Ramond black hole on neutrino behavior, Journal of High Energy Physics2025, 028 (2025), arXiv:2504.15373

    2025 arXiv

  52. [60]

    A. A. Araújo Filho, N. Heidari, and J. A. A. S. Reis, The impact of an antisymmetric tensor on charged black holes: evaporation process, geodesics, deflection angle, scattering effects and quasinormal modes, Classical and Quantum Gravity 42, 065026 (2025)

    2025

  53. [61]

    A. A. Araújo Filho, N. Heidari, and I. P. Lobo, A non-commutative Kalb–Ramond black hole, Journal of Cosmology and Astroparticle Physics2025(09), 076, arXiv:2507.17390

  54. [62]

    A. A. Araújo Filho, Antisymmetric tensor influence on charged black hole lensing phenomena and time delay, Journal of High Energy Astrophysics47, 100401 (2025), arXiv:2406.11582

    2025 arXiv

  55. [63]

    C. F. S. Pereira, M. V. de S. Silva, A. R. Soares, A. A. Araújo Filho, R. L. L. Vitória, and H. Belich, Light propagation and gravitational lensing effects in charged Kalb–Ramond spacetime in nonlinear electrodynamics, Physics Letters B879, 140699 (2026), arXiv:2602.22905

    2026 arXiv

  56. [64]

    A. A. Araújo Filho, N. Heidari, I. P. Lobo, and Y. Shi, Optical phenomena in a non-commutative Kalb–Ramond black hole spacetime, Annals of Physics492, 170550 (2026), arXiv:2508.08889

    2026 arXiv

  57. [65]

    Mangut and I

    M. Mangut and I. Sakalli, Lorentz-symmetry violation in charged black-hole thermodynamics and gravitational lensing: effects of the kalb–ramond field, Chinese Physics C49, 065106 (2025)

    2025

  58. [66]

    Y. T. Gu, W.-D. Guo, and Y.-X. Liu, Quasinormal modes of an electrically charged kalb–ramond black hole, Chinese Physics C 10.1088/1674-1137/ae6ed3 (2026)

    2026 doi

  59. [67]

    R. M. Zulqarnain, O. Donmez, and G. Mustafa, Influence of nonlinear electrodynamics on time-dependent accretion dynamics around kalb–ramond black hole, Chinese Physics C50, 085107 (2026)

    2026

  60. [68]

    Jumaniyozov, S

    S. Jumaniyozov, S. U. Khan, J. Rayimbaev, A. Abdujabbarov, S. Urinbaev, and S. Murodov, Circular motion and qpos near black holes in kalb–ramond gravity, The European Physical Journal C84, 964 (2024)

    2024

  61. [69]

    Jumaniyozov, M

    S. Jumaniyozov, M. Zahid, M. Alloqulov, I. Ibragimov, J. Rayimbaev, and S. Murodov, Radiative properties and qpos around charged black hole in kalb–ramond gravity, The European Physical Journal C85, 126 (2025)

    2025

  62. [70]

    Jumaniyozov, S

    S. Jumaniyozov, S. Murodov, J. Rayimbaev, I. Ibragimov, B. Madaminov, S. Urinbaev, and A. Abdujabbarov, Black holes surrounded by pfdm in kalb–ramond gravity: from thermodynamics to qpo tests, The European Physical Journal C85, 28 797 (2025)

    2025

  63. [71]

    Rahmatov, I

    B. Rahmatov, I. Egamberdiev, S. Murodov, J. Rayimbaev, I. Ibragimov, E. Davletov, and S. Djumanov, Gravitational lensing by black holes surrounded by pfdm in kalb–ramond gravity in plasma medium, Physics of the Dark Universe50, 102152 (2025)

    2025

  64. [72]

    Murodov, J

    S. Murodov, J. Rayimbaev, and B. Ahmedov, Quasiperiodic oscillations and dynamics of test particles around quasi- and non-schwarzschild black holes, Universe9, 391 (2023)

    2023

  65. [73]

    Rahmatov, M

    B. Rahmatov, M. Zahid, J. Rayimbaev, R. Rahim, and S. Murodov, Qpos and circular orbits around black holes in chaplygin-like cold dark matter, Chinese Journal of Physics92, 143 (2024)

    2024

  66. [74]

    Rahmatov, S

    B. Rahmatov, S. Murodov, and O. Umarov, Thermodynamics and qpo signatures of rotating kazakov–solodukhin quantum black holes, The European Physical Journal Plus141, 10.1140/epjp/s13360-026-08024-6 (2026)

    2026 doi

  67. [75]

    C.-Y. Yang, K. He, and X.-X. Zeng, Observational signatures and polarized images of rotating charged black holes in kalb–ramond gravity, The European Physical Journal C 10.1140/epjc/s10052-026-15688-y (2026)

    2026 doi

  68. [76]

    Yao, K.-J

    J.-T. Yao, K.-J. He, Z.-C. Lin, and H. Yu, Energy extraction from rotating charged black holes in kalb–ramond gravity, Physics Letters B878, 140562 (2026)

    2026

  69. [77]

    Armas, Y

    J. Armas, Y. Cai, G. Compere, D. Garfinkle, and S. E. Gralla, Consistent blandford–znajek expansion, Journal of Cos- mology and Astroparticle Physics2020(04), 009

  70. [78]

    S. S. Komissarov, Blandford–znajek mechanism versus penrose process, Journal of the Korean Physical Society54, 2503 (2009)

    2009

  71. [79]

    D. W. Hogg, J. Bovy, and D. Lang, Data analysis recipes: Fitting a model to data (2010), arXiv:1008.4686 [astro-ph.IM]

    2010 arXiv

  72. [80]

    Trotta, Bayesian methods in cosmology (2017), arXiv:1701.01467 [astro-ph.CO]

    R. Trotta, Bayesian methods in cosmology (2017), arXiv:1701.01467 [astro-ph.CO]

    2017 arXiv

  73. [81]

    S. N. Zhanget al., Broadband high-energy observations of the superluminal jet source gro j1655–40 during an outburst, The Astrophysical Journal479, 381 (1997)

    1997

  74. [82]

    R. A. Remillardet al., Rxte observations of 0.1–300 hz quasi-periodic oscillations in the microquasar gro j1655–40, The Astrophysical Journal522, 397 (1999)

    1999

  75. [83]

    Gierlinski, A

    M. Gierlinski, A. Maciolek-Niedzwiecki, and K. Ebisawa, Application of a relativistic accretion disc model to x-ray spectra of lmc x-1 and gro j1655–40, Monthly Notices of the Royal Astronomical Society325, 1253 (2001)

    2001

  76. [84]

    J. A. Tomsicket al., Broadband x-ray spectra of the black hole candidate gro j1655–40, The Astrophysical Journal512, 892 (1999)

    1999

  77. [85]

    Greiner, J.-G

    J. Greiner, J.-G. Cuby, and M. J. McCaughrean, An unusually massive stellar black hole in the galaxy, Nature414, 522 (2001)

    2001

  78. [86]

    S. N. Zhang, W. Cui, and W. Chen, Three-layered atmospheric structure in accretion disks around stellar-mass black holes, Science287, 1239 (2000)

    2000

  79. [87]

    Narayan and J

    R. Narayan and J. E. McClintock, Observational evidence for a correlation between jet power and black hole spin, Monthly Notices of the Royal Astronomical Society Letters419, L69 (2012)

    2012

  80. [88]

    J. F. Steiner, J. E. McClintock, and R. Narayan, Jet power and black hole spin: Testing an empirical relationship and using it to predict the spins of six black holes, The Astrophysical Journal762, 104 (2012)

    2012

  81. [89]

    J. E. McClintock, R. Narayan, and J. F. Steiner, Black hole spin via continuum fitting and the role of spin in powering transient jets, Space Science Reviews183, 295 (2014)

    2014

  82. [90]

    Zhang and W

    H. Zhang and W. Yu, Discovery of the correlation between peak episodic jet power and x-ray peak luminosity of the soft state in black hole transients, Monthly Notices of the Royal Astronomical Society451, 1740 (2015)

    2015

  83. [91]

    Feng and Q

    J. Feng and Q. Wu, Constraint on the black-hole spin of m87 from the accretion-jet model (2017), arXiv:1705.07804 [astro-ph.HE]

    2017 arXiv

  84. [92]

    van Velzen and H

    S. van Velzen and H. Falcke, The contribution of spin to jet-disk coupling in black holes, Astronomy and Astrophysics 557, L7 (2013)

    2013

  85. [93]

    R. A. Daly, Spin properties of supermassive black holes with powerful outflows, Monthly Notices of the Royal Astronomical Society Letters458, L24 (2016)

    2016

  86. [94]

    J. C. McKinney, M. O’Riordan, and A. Pe’er, Effects of spin on high-energy radiation from accreting black holes, The Astrophysical Journal831, 62 (2016)

    2016

  87. [95]

    Foreman-Mackey, D

    D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The mcmc hammer, Publications of the Astronomical Society of the Pacific125, 306 (2013)

    2013

  88. [96]

    Huijser, J

    D. Huijser, J. Goodman, and B. J. Brewer, Properties of the affine invariant ensemble sampler’s stretch move in high dimensions (2017), arXiv:1509.02230 [stat.CO]

    2017 arXiv

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