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

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 $θ{\rm sh}$ of M87* at inclination $θ_o=17^\circ$ and fixed $Q=0.2$, the EHT-allowed range $θ{\rm sh}\in(35.1,\,40.5)\,μ\mathrm{as}$ 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 $θ{\rm sh}$ of Sgr A* at inclination $θ_o=50^\circ$ and fixed $Q=0.2$, the corresponding EHT-allowed range $θ{\rm sh}\in(41.7,\,55.7)\,μ\mathrm{as}$ 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.

• The paper derives rotating, charged black hole solutions in Kalb-Ramond gravity using a modified Newman-Janis algorithm.
• It demonstrates how the Lorentz-violating parameter and electric charge modify horizon structures and photon shadow geometries.
• Results constrain the parameter l with EHT observations, illustrating KR gravity as a viable quantum gravity-inspired modification.

Summary of "Probing Kalb-Ramond Gravity with Charged Rotating Black Holes: Constraints from EHT Observations"

Motivation and Framework

The paper investigates charged rotating black holes in Kalb-Ramond (KR) gravity, a modified gravity scenario motivated by string theory that incorporates spontaneous Lorentz symmetry breaking. The KR field, an antisymmetric tensor intrinsic to string theory, can acquire a non-zero vacuum expectation value, yielding Lorentz-violating effects in the low-energy gravitational regime. The authors construct black hole solutions characterized by three parameters: mass $M$, spin $a$, electric charge $Q$, and a Lorentz-violating parameter $l$ that deforms the standard Kerr-Newman metric via a radial-dependent mass function. Nonminimal couplings between the KR field and the spacetime curvature modify gravitational dynamics, enabling deviations from General Relativity (GR) at horizon scales.

Solution Construction and Parameter Space

Using the modified Newman-Janis algorithm, the authors derive axially symmetric metrics for rotating, charged KR black holes. The horizon structure is altered compared to Kerr-Newman: both $Q$ and $l$ shrink the domain of allowed high-spin configurations where event horizons persist, leading to parameter-dependent transitions between black hole and horizonless regimes. The modification of the mass function by $l$ yields spacetime anisotropies and affects null geodesics, photon regions, and the associated shadow morphology.

For a fixed $Q$, increasing $l$ reduces the maximal allowed spin before the horizon vanishes. For a fixed $l$, increasing $a$0 reduces the spin interval supporting regular black holes. This interplay constrains the astrophysically relevant parameter space and requires careful delineation of horizon and photon ring boundaries.

Geometric Analysis of Photon Regions and Shadows

The KR black hole spacetime admits separable null geodesics characterized by energy, axial angular momentum, and Carter constant. The photon region, central to shadow formation, is distorted by both $a$1 and $a$2. As $a$3 increases, frame-dragging shifts prograde photon orbits inward toward the horizon, while retrograde orbits are displaced outward, rendering the photon shell and shadow increasingly asymmetric.

The Lorentz-violating parameter $a$4 reduces the shadow radius by a factor $a$5, a strong claim supported by explicit orbital calculations, while $a$6 introduces additional distortions. In horizonless configurations, closed photon rings persist for a limited range of $a$7, yielding dark silhouettes even without event horizons—a property distinguishing KR black holes from conventional naked singularities in Kerr or Reissner-Nordström spacetimes.

Shadow Observables and Parameter Estimation

Shadow-based parameter estimation leverages observables such as area ($a$8), oblateness ($a$9), radius ($Q$0), and distortion ($Q$1) to constrain $Q$2 and $Q$3. The robust Ghosh-Kumar framework is applied, extracting geometric shadow parameters from celestial coordinates and eliminating degeneracies not resolved by the traditional Hioki-Maeda descriptors. This methodology is crucial for quantifying deviations that can be traced directly to underlying theory parameters.

The impact of $Q$4 is prominent: increasing $Q$5 enlarges the shadow area despite simultaneously reducing the event horizon area—a geometric effect decoupled from the physical horizon, emphasizing the relevance of KR modifications to observable photon regions. Charge $Q$6 does not dominate the shadow morphology but tightens the window for allowed $Q$7, especially at high spin.

Thermal Energy Emission

The absorption cross-section in the high-energy limit is governed by the shadow radius, linking shadow geometry to Hawking temperature and spectral characteristics. The Lorentz-violating $Q$8 modifies both the horizon structure and photon region, controlling the emission rate via its effect on $Q$9 and $l$0. Increasing $l$1 suppresses spectral peaks, and $l$2 modulates both the position and amplitude of the emission spectrum—a dual impact with measurable consequences for future direct spectral observations.

EHT Observational Constraints

EHT imaging of M87* and Sgr A* provides angular diameter bounds for black hole shadows, enabling direct constraints on $l$3. The analysis applies both the shadow area and oblateness technique and the fractional Schwarzschild deviation parameter $l$4. For M87* ($l$5, $l$6), the EHT-allowed shadow diameter range constrains $l$7 to $l$8 (low spin) and $l$9 (high spin). For Sgr A* ($Q$0, $Q$1), the allowed region is $Q$2, and using stellar dynamics mass prior yields upper bounds of $Q$3. Increasing $Q$4 slightly tightens and shifts these bounds.

Across all parameter regimes explored, the KR black hole solutions are consistent with EHT data, indicating that Lorentz-violating gravity is not observationally excluded for a substantial interval of $Q$5. However, parameter bounds are not extremely tight, reflecting current uncertainties and measurement precision.

Implications and Future Prospects

The results validate the utility of horizon-scale black hole imaging as a practical tool for constraining Lorentz violation at Planck-scale sensitivity. The charged rotating KR black hole survives as an observationally viable alternative to Kerr, with explicit parameter constraints dictated by real EHT data. Practically, this opens the path for astrophysical probes of string-inspired Lorentz symmetry breaking.

Theoretically, the KR gravity construction exemplifies how modified gravity can impact observable photon regions and thermodynamic properties without grossly violating GR in the weak-field regime. Closed photon rings in horizonless configurations offer testable predictions distinguishing KR from Kerr, especially as future ngEHT or space-based interferometers improve resolution.

A significant implication is the necessity for including GRMHD effects in the construction of KR-specific image libraries, as current shadow calculations neglect astrophysical plasma and variability. The methodology outlined provides a blueprint for rigorous parameter estimation in other modified gravity frameworks.

Future developments will focus on refining observational constraints with higher precision imaging, expanding parameter scans to incorporate additional perturbations, and exploring spectral signatures directly linked to $Q$6. As measurement sensitivity improves, the allowed interval for Lorentz-violating parameters will become increasingly stringent, with potential to rule in or out theories motivated by quantum gravity.

Conclusion

Charged rotating black holes in KR gravity, defined by spin, charge, and Lorentz-violating tensor fields, exhibit distinctive shadow and thermodynamic features distinguishable from Kerr black holes. Analyses of EHT observations yield direct constraints on the Lorentz-violating scale $Q$7, demonstrating consistency with current data and providing a new avenue for astrophysical tests of quantum gravity-inspired modifications. The combined geometric and thermodynamic approach underscores the future promise of black hole imaging as a probe of fundamental spacetime structure.