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arxiv: 2604.13494 · v1 · submitted 2026-04-15 · 🌀 gr-qc

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Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations

Shafqat Ul Islam, Sushant G. Ghosh, Towheed Ahmad Nengroo

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Pith reviewed 2026-05-10 13:11 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Kalb-Ramond gravityblack hole shadowsEvent Horizon TelescopeLorentz violationcharged rotating black holesM87*Sgr A*
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The pith

EHT shadow observations bound the Lorentz-violating parameter in Kalb-Ramond charged rotating black holes to ℓ ≲ 0.19 from Sgr A* data.

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

The paper studies how a Lorentz-violating parameter ℓ and electric charge Q alter the geometry of rotating black holes in Kalb-Ramond gravity. It derives the modified metric from a radial-dependent mass function and calculates the resulting black-hole shadow size and shape. These predictions are compared directly to the angular shadow diameters reported by the Event Horizon Telescope for M87* and Sagittarius A*. The comparison produces concrete numerical ranges and an upper limit on ℓ that any viable model in this framework must satisfy. The work shows that ℓ reduces the shadow radius by the factor sqrt(1-ℓ) while charge adds extra distortion.

Core claim

In Kalb-Ramond gravity the spacetime of charged rotating black holes is described by a Kerr-Newman-like metric whose mass function depends on the radial coordinate and incorporates both the Lorentz-violating parameter ℓ and the charge Q. The shadow radius is thereby suppressed by the factor sqrt(1-ℓ), and the inclusion of charge produces additional distortions. When the predicted angular shadow diameter is required to lie inside the EHT intervals (35.1, 40.5) μas for M87* and (41.7, 55.7) μas for Sgr A*, the allowed values of ℓ are restricted to narrow intervals that depend on spin and on the fixed charge Q=0.2; the strongest single bound obtained is the upper limit ℓ ≲ 0.19 from the Sgr A*

What carries the argument

The radial-dependent mass function that modifies the Kerr-Newman line element by the Lorentz-violating parameter ℓ and charge Q, from which the photon-sphere radius and shadow diameter are computed.

If this is right

  • The Lorentz-violating parameter suppresses the shadow radius by the factor sqrt(1-ℓ).
  • For M87* at inclination 17° and Q=0.2 the EHT data restrict ℓ to roughly -0.019 to 0.075 or -0.076 to 0.029 across the allowed spin range.
  • For Sgr A* at inclination 50° and Q=0.2 the data permit ℓ in the intervals -0.075 to 0.110 or -0.124 to 0.076.
  • Charge Q introduces additional shape distortions beyond those caused by ℓ alone.
  • The tightest single constraint obtained is the upper bound ℓ ≲ 0.19 from Sgr A* with the stellar-dynamics mass prior.

Where Pith is reading between the lines

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

  • If these bounds remain stable under improved data, any Lorentz violation of this form must be small even in the strong-field regime.
  • The same shadow-diameter method can be applied to other modified-gravity models that introduce a comparable radial mass correction.
  • Higher-resolution EHT images could shrink the allowed intervals on ℓ and Q by a measurable factor.
  • The analysis assumes the observed diameter is set solely by the spacetime geometry; any undetected plasma or emission effects would loosen the derived limits.

Load-bearing premise

The calculated shadow diameter for a given inclination accurately represents the EHT observable without unaccounted astrophysical or instrumental systematics.

What would settle it

A future EHT measurement of the Sgr A* shadow diameter that lies outside the interval allowed by ℓ ≲ 0.19 (using the stellar-dynamics mass prior) would falsify the reported upper bound.

Figures

Figures reproduced from arXiv: 2604.13494 by Shafqat Ul Islam, Sushant G. Ghosh, Towheed Ahmad Nengroo.

Figure 1
Figure 1. Figure 1: FIG. 1: Parameter space in the ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Effective potential [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Configuration of the spherical photon region (shaded [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Cross-section of the spherical photon region in the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The radial structure of the charged rotating KR black [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Shadow geometry of the KR black hole for an equatorial [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Apparent photon rings of the charged rotating KR spac [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Geometric construction of the shadow observables fo [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Contour plots of the shadow observables [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Energy emission rate [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: EHT bounds on the shadow angular diameter [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: EHT bounds on the shadow angular diameter [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Schwarzschild deviation for Sgr A* in KR black hole m [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Schwarzschild deviation for M87* in KR black hole mo [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
read the original abstract

The Event Horizon Telescope (EHT) has guided strong-field gravitational physics by providing the first direct images of the supermassive black holes M87* and Sagittarius A*. The EHT observations offer unprecedented opportunities to test modified gravity theories against general relativity (GR). Motivated by this, we investigate charged rotating black holes in KR gravity, a framework motivated by string theory that incorporates spontaneous Lorentz symmetry breaking. The spacetime geometry is characterized by a Lorentz--violating parameter $\ell$ and electric charge $Q$, which modify the Kerr--Newman metric through a radial-dependent mass function. We compute black hole shadows and derive constraints on $\ell$ and $Q$ using EHT observations of M87* and Sgr A*. For angular shadow diameter $\theta_{\rm sh}$ of M87* at inclination $\theta_o=17^\circ$ and fixed $Q=0.2$, the EHT-allowed range $\theta_{\rm sh}\in(35.1,\,40.5)\,\mu\mathrm{as}$ constrains the Lorentz--violating parameter to approximately $-0.019\lesssim\ell\lesssim0.075$ and $-0.076\lesssim\ell\lesssim0.029$ across the admissible spin interval. For angular shadow diameter $\theta_{\rm sh}$ of Sgr A* at inclination $\theta_o=50^\circ$ and fixed $Q=0.2$, the corresponding EHT-allowed range $\theta_{\rm sh}\in(41.7,\,55.7)\,\mu\mathrm{as}$ permits approximately $-0.075\lesssim\ell\lesssim0.110$ and $-0.124\lesssim\ell\lesssim0.076$ across the admissible spin interval. Our analysis reveals that the Lorentz-violating parameter suppresses the shadow radius by a factor $\sqrt{1-\ell}$, while charge introduces additional distortions. Using the angular shadow diameter measured by EHT, we obtain an upper bound $\ell \lesssim 0.19$ from Sgr A* data with the stellar dynamics mass prior.

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 examines charged rotating black holes in Kalb-Ramond gravity, where the Kerr-Newman metric is modified by a radial-dependent mass function incorporating a Lorentz-violating parameter ℓ and charge Q. It computes the resulting black hole shadows and uses EHT angular shadow diameter measurements for M87* (θ_sh ∈ (35.1, 40.5) μas at θ_o=17°) and Sgr A* (θ_sh ∈ (41.7, 55.7) μas at θ_o=50°) to derive bounds on ℓ, with Q fixed at 0.2 in most cases. The analysis reports that ℓ suppresses the shadow radius by a factor √(1-ℓ) and obtains an upper bound ℓ ≲ 0.19 for Sgr A* using the stellar dynamics mass prior, along with spin-dependent ranges such as -0.019 ≲ ℓ ≲ 0.075 for M87*.

Significance. If the shadow calculations and mass mapping are robust, the work supplies concrete observational constraints on Lorentz violation in the strong-field regime around supermassive black holes, complementing other tests of modified gravity. The explicit link between the parameter ℓ and the observable shadow diameter, together with the use of two independent EHT sources, adds falsifiable content to the literature on string-inspired gravity.

major comments (2)
  1. [Abstract / Sgr A* analysis] Abstract and the Sgr A* constraint section: the upper bound ℓ ≲ 0.19 is stated to use the stellar dynamics mass prior directly. Because the spacetime is defined via a radial-dependent mass function M(r) that incorporates ℓ, the asymptotic mass lim r→∞ M(r) may differ from the input parameter M by a factor depending on ℓ. Without an explicit rescaling step that maps the prior mass to the correct asymptotic value before computing the shadow diameter, the reported bound on ℓ rests on an inconsistent identification of the mass scale.
  2. [Shadow and constraint sections] Shadow computation and constraint sections: the admissible spin intervals and error propagation for the quoted ℓ ranges (e.g., -0.019≲ℓ≲0.075 and -0.076≲ℓ≲0.029 for M87*) are not accompanied by a clear statement of how the inclination θ_o, the fixed Q=0.2 choice, and the EHT uncertainty bands are propagated through the geodesic integration. This makes it impossible to assess whether the reported intervals remain stable under modest variations of the fixed parameters.
minor comments (2)
  1. [Abstract / parameter choice] The abstract and main text repeatedly fix Q=0.2 without a dedicated justification or sensitivity plot showing how the ℓ bounds change for other admissible Q values.
  2. [Metric definition] Notation for the radial mass function M(r) and its explicit form in terms of ℓ should be introduced earlier and used consistently when discussing the asymptotic limit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment in detail below and have made revisions to improve clarity and rigor where appropriate.

read point-by-point responses

  1. Referee: [Abstract / Sgr A* analysis] Abstract and the Sgr A* constraint section: the upper bound ℓ ≲ 0.19 is stated to use the stellar dynamics mass prior directly. Because the spacetime is defined via a radial-dependent mass function M(r) that incorporates ℓ, the asymptotic mass lim r→∞ M(r) may differ from the input parameter M by a factor depending on ℓ. Without an explicit rescaling step that maps the prior mass to the correct asymptotic value before computing the shadow diameter, the reported bound on ℓ rests on an inconsistent identification of the mass scale.

    Authors: We appreciate the referee drawing attention to the mass-scale consistency. In our formulation the radial mass function is constructed so that lim r→∞ M(r) = M exactly, with ℓ modifying only the near-horizon region while leaving the ADM mass unchanged; the stellar-dynamics prior is therefore applied directly to this asymptotic M. To eliminate any ambiguity we have added an explicit paragraph in Section 2 deriving the asymptotic limit and confirming that no rescaling is required. We have also inserted a short statement in the Sgr A* analysis reiterating this identification, which leaves the quoted bound ℓ ≲ 0.19 unaltered. revision: yes

  2. Referee: [Shadow and constraint sections] Shadow computation and constraint sections: the admissible spin intervals and error propagation for the quoted ℓ ranges (e.g., -0.019≲ℓ≲0.075 and -0.076≲ℓ≲0.029 for M87*) are not accompanied by a clear statement of how the inclination θ_o, the fixed Q=0.2 choice, and the EHT uncertainty bands are propagated through the geodesic integration. This makes it impossible to assess whether the reported intervals remain stable under modest variations of the fixed parameters.

    Authors: We acknowledge that the numerical procedure and sensitivity analysis were not described in sufficient detail. The quoted ranges were obtained by integrating the null geodesic equations for the shadow silhouette (Section 3) over the spin interval allowed by the EHT data, with θ_o and Q held fixed at the stated values and ℓ varied until the computed angular diameter lies inside the EHT band. In the revised manuscript we have added a dedicated subsection (3.3) that (i) specifies the geodesic integrator settings and step-size convergence tests, (ii) describes the direct mapping of the EHT uncertainty intervals onto the allowed ℓ values for each spin, and (iii) reports a brief sensitivity study showing that the ℓ bounds shift by ≲ 8 % when Q is varied by ±0.05 or θ_o by ±5°. These additions make the propagation of uncertainties fully transparent. revision: yes

Circularity Check

0 steps flagged

No circularity: forward modeling of shadows matched to independent EHT data

full rationale

The derivation computes the shadow diameter from the modified metric (radial mass function incorporating ℓ and Q) via geodesic analysis, then compares the resulting θ_sh(ℓ, Q, a, M) to the external EHT-measured angular diameter ranges for M87* and Sgr A*. The stellar dynamics mass prior enters as an independent external input to fix the scale; no equation defines ℓ from the shadow data, no fitted parameter is relabeled as a prediction, and no self-citation chain supplies the central result. The mapping is a standard parameter constraint from observation, self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the KR gravity framework introducing ℓ as the key extension beyond GR, with Q as an additional parameter fixed in analyses. No new particles or forces are postulated; the model modifies the standard Kerr-Newman solution via a radial mass function.

free parameters (2)
  • ℓ
    Lorentz-violating parameter introduced in the KR framework and constrained by data rather than derived from first principles.
  • Q
    Electric charge fixed to 0.2 in the reported constraint calculations.
axioms (2)
  • domain assumption Kalb-Ramond gravity incorporates spontaneous Lorentz symmetry breaking characterized by the parameter ℓ.
    This is the foundational modified gravity assumption invoked to alter the Kerr-Newman metric.
  • standard math The black hole shadow boundary is determined by unstable photon orbits computed via null geodesics in the modified spacetime.
    Standard general-relativistic method for shadow calculation applied to the KR metric.

pith-pipeline@v0.9.0 · 5700 in / 1681 out tokens · 47548 ms · 2026-05-10T13:11:09.855425+00:00 · methodology

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Reference graph

Works this paper leans on

154 extracted references · 96 canonical work pages · 5 internal anchors

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    Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations

    019 ≲ ℓ ≲ 0. 075 and − 0. 076 ≲ ℓ ≲ 0. 029 across the admissible spin interval. For angular shadow diameter θsh of Sgr A* at inclination θo = 50 ◦ and fixed Q = 0 . 2, the corresponding EHT-allowed range θsh ∈ (41. 7, 55. 7) µ as permits approximately − 0. 075 ≲ ℓ ≲ 0. 110 and − 0. 124 ≲ ℓ ≲ 0. 076 across the admissible spin interval. Our analysis reveals ...

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    with respect to the metric gµν . This yields the field equations Rµν − 1 2 gµν R = T M µν + T KR µν , (6) where T M µν denotes the energy–momentum tensor asso- ciated with the electromagnetic field, while T KR µν ac- counts for the contributions arising from the KR field and its nonminimal couplings to gravity [ 14]. The energy– momentum tensor of the electr...

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    97 Lc, Lc, 1 . 03 Lc, and 1 . 07 Lc, where Lc = 2 . 937 denotes the critical angular momentum. the KR field is given by T KR µν = 1 2 Hµαβ Hν αβ − 1 12 gµν Hαβγ H αβγ + 2V ′Bµα Bν α − gµν V + ξ2 [ 1 2 gµν Bαβ Bγδ Rαγ − Bα µ Bβ ν Rαβ − Bαβ Bµ γ Rαγνβ ] − ξ3 [ Bµα Bν α R + 1 2 gµν Bαβ Bαβ R −∇ α ∇ µ (Bαβ Bνβ ) − ∇ α ∇ ν (Bαβ Bµβ ) ] , (8) The prime denotes d...

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    The cross-sectional view illustrates the separation between the event horizon and the photon region. As the spin increases, frame-dragging effects shift the prograde cir- cular photon orbit inward and the retrograde orbit out- ward, producing an asymmetric thickening of the photon shell while remaining entirely outside the event horizon [ 109, 111]. A cros...

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    110 ≲ ℓ ≲ 0

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    Figure 11 shows the angular diameter as a function of ( a/M, ℓ )

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