EHT-Constrained Analysis of Shadow Deformation in Quantum-Improved Rotating Non-Singular Magnetic Monopole

Abstract: We studied the shadow cast by a rotating Bardeen black hole within the framework of asymptotically safe gravity. The null geodesics were analyzed using the Hamilton Jacobi separation method to derive shadow observables. Our findings show that an increase in both the asymptotic safety parameter and the spin parameter leads to a decrease in the apparent shadow size and an increase in shadow distortion. The monopole charge of the black hole played an important role in the shadow profile. Furthermore, we compute the energy emission rate associated with varying values of the asymptotic safety parameter.

• The paper demonstrates that quantum corrections via asymptotically safe gravity regularize the Bardeen metric to yield non-singular, rotating black holes.
• Employing the Newman–Janis algorithm, the study derives explicit shadow boundaries and angular parameters consistent with EHT observations.
• Numerical analysis reveals that increased quantum couplings and spin modify shadow distortion and energy emission, aligning with observational constraints.

EHT-Constrained Analysis of Shadow Deformation in Quantum-Improved Rotating Non-Singular Magnetic Monopole

Introduction

This work presents an analytical investigation of the shadow properties and energy emission of rotating regular (non-singular) Bardeen black holes within the framework of asymptotically safe gravity (ASG). The study leverages the recent observational results from the Event Horizon Telescope (EHT) targets M87* and Sgr A*, imposing new constraints on model parameters arising from quantum gravity corrections, black hole spin, and magnetic monopole charge.

The motivation is anchored in the limitations of General Relativity (GR) in the quantum regime, particularly the breakdown near classical singularities. Asymptotic Safety, which posits a non-Gaussian ultraviolet fixed point in the renormalization group flow of gravitational couplings, provides an effective avenue for quantum-improved black hole metrics, in principle allowing for singularity resolution and tangible phenomenological consequences at observable scales.

Quantum-Improved Bardeen Black Holes in ASG

RG-Improved Gravity and the Running Newton Constant

The study employs the Einstein–Hilbert truncation in Quantum Einstein Gravity (QEG) to generate a scale-dependent Newton constant $G(k)$, subsequently mapped to a coordinate-dependent function $G(r)$ using an invariant proper distance cutoff identification. The beta-function analysis exhibits two fixed points: a trivial infrared Gaussian fixed point and a non-Gaussian ultraviolet fixed point governing the ultraviolet behavior. The result is a gravitational coupling $G(r)$ that weakens at short distances, implementing quantum corrections to the classical gravitational field consistent with ASG expectations.

For the Bardeen metric, incorporating a nonlinear electromagnetic source, the RG-improved running of $G(r)$ is shown to regularize the spacetime, allowing for consistent extension to high-curvature regimes. The impact of non-universality from the cutoff function and phenomenological parameters is addressed, noting that specific parameter values must ultimately be constrained through observational input.

Rotating Extension via Newman–Janis Algorithm

The Bardeen metric, already non-singular and free from classical curvature singularities, is algorithmically generalized to the rotating case via the Newman–Janis technique. The resulting metric displays the characteristic structure of a regular Kerr-like black hole with quantum-improved mass and coupling functions. The spacetime is parameterized by mass $M$, spin $a$, magnetic monopole charge $g$, and two ASG couplings $(\omega, \gamma)$.

Black Hole Shadow Formation and Observables

Null Geodesics and Shadow Contours

Adopting the Hamilton–Jacobi formalism, the null geodesic equations are separated to calculate critical impact parameters determining the unstable photon orbits, which in turn trace the observable shadow boundary. The model encapsulates both the frame dragging from rotation and the curvature corrections from quantum gravity and non-linear electrodynamics.

Explicit expressions for impact parameters $(\xi, \eta)$, as well as the celestial coordinates $(\alpha, \beta)$ describing the shadow, are derived. The boundary is sensitive to the quantum parameters, monopole charge, and the inclination angle of observation.

Influence of Parameters on Shadow Deformation

Numerical analysis reveals that increasing the quantum coupling parameters $G(r)$0 and spin $G(r)$1 generally reduces the shadow size and increases distortion. The monopole charge $G(r)$2 introduces additional, but sub-leading, deformation effects, increasingly pronounced at high spin. These results are in accord with the qualitative expectation that strong quantum gravity corrections and deviating electromagnetic structure modulate the near-horizon geometry, although the paper notes a limited effect of the quantum couplings on the shadow radius, with more significant impact on shadow distortion at large $G(r)$3 and $G(r)$4.

Shadow Circularity and Observational Constraints

Quantitative metrics such as the deviation from circularity $G(r)$5 and the fractional deviation of shadow diameter $G(r)$6 (relative to Schwarzschild) are evaluated. These are directly compared with EHT constraints obtained from M87* and Sgr A*, specifically $G(r)$7 and $G(r)$8. The analysis demonstrates that the model parameters remain consistent with all current EHT bounds, and provides exclusion contours on the $G(r)$9 parameter spaces. In particular, the study finds that $G(r)$0, $G(r)$1, with all viable $G(r)$2 combinations lying within allowable observational regimes for both moderate and high inclination (up to $G(r)$3).

Energy Emission and Hawking Radiation

The energy emission rate, calculated in the standard framework of semi-classical Hawking radiation, is shown to be sensitive to the same set of parameters. The inclusion of quantum gravitational running and monopole charge alters the graybody factors, modifying the emission spectrum. Notably, increasing spin suppresses the high-frequency emission, whereas larger monopole charge enhances the emission peak, a result that could be significant for signatures of regular black holes in the context of future precision black hole spectroscopy.

Implications and Future Directions

This work provides a detailed mapping between quantum gravity-corrected black hole parameters and direct EHT observables. The results demonstrate that regular Bardeen black holes in ASG with a limited range of $G(r)$4 remain compatible with the detected horizon-scale images of M87* and Sgr A*, constraining deviations from both the Schwarzschild and Kerr paradigms. On the theoretical side, the study solidifies the use of ASG as a phenomenologically viable quantum gravity scenario with testable consequences in astrophysical environments.

From a practical standpoint, the limitations imposed on quantum parameters from shadow morphology can potentially guide future model-building in quantum gravity and may become tighter as EHT and next-generation VLBI observations accumulate more precise data, particularly at higher inclinations and for other systems.

In the context of quantum black hole phenomenology, the connection between the running of the gravitational constant, regular horizons, and their radiative characteristics opens the door to further studies on dynamical signatures (e.g., quasi-normal modes) and high-frequency gravitational wave emission, extending beyond mere shadow morphology.

Conclusion

The analysis rigorously demonstrates that quantum-improved rotating Bardeen black holes in the context of asymptotically safe gravity are consistent with current observational data from EHT. Significant constraints are placed on the quantum and electromagnetic parameters governing departures from classical GR. The study elucidates the robust, parameter-dependent interplay between strong gravity, quantum corrections, and electromagnetic structure in shaping black hole observables, and sets a solid baseline for ongoing and future tests of quantum gravity via black hole imaging and radiation phenomena.

Reference: "EHT-Constrained Analysis of Shadow Deformation in Quantum-Improved Rotating Non-Singular Magnetic Monopole" (2604.04695).