Testing loop quantum gravity through EHT observations of M87* and Sgr A* using rotating holonomy-corrected black holes

Abstract: The Event Horizon Telescope (EHT) has provided a new tool for testing the strong-field regime of gravity by imaging the shadows of M87* and Sgr A*. These observations provide the first real opportunity to test whether quantum gravity--specifically loop quantum gravity--leaves observable imprints on spacetime. We use the EHT observations of M87* and Sgr A* to examine the observational signs of rotating holonomy-corrected black holes (RHCBHs). We discover that, in comparison to the typical Kerr black hole, the quantum correction parameter $b$ increases the size of the black hole shadow. As the deviation parameter $b$ increases in RHCBH, the prograde photon orbits shift outward, indicating a weaker effective gravitational field near the central region. Unlike Kerr naked singularities, which produce open arc-like shadows, the RHCBH spacetime can still produce closed shadow rings even in the absence of an event horizon. We find that photon rings continue to exist in the parameter range $b_E \leq b \leq b_p$, due to the presence of unstable circular photon orbits.We apply the Kumar--Ghosh method based on the shadow observables: the shadow area $A$ and the oblateness $D$ that together allow a unique determination of the spin parameter $a$ and the quantum correction parameter $b$. At $θ_o=17$\textdegree~, the angular diameter bound of M87$^{*}$ yields $b \leq 0.1319\,M$ at $a = 0\,$ and $b \leq 0.421\,M$ at $a = 0.784\,M$, while at $θ_o=50$\textdegree~, the angular diameter bound of Sgr A$^{*}$ yields $b \leq 0.5764\,M$ at $a = 0\,$ and $b \leq 0.7482\,M$ at $a = 0.6253\,M$ the Sgr~A$^{*}$. Our results show that nonzero values of the holonomy correction parameter are consistent with current EHT data, indicating that RHCBHs provide viable alternatives to the classical Kerr geometry in the strong-gravity regime and are strong astrophysical black hole candidates.

• The paper introduces a rotating holonomy-corrected black hole metric that incorporates a quantum correction parameter to modify classical Kerr geometries.
• It employs the Kumar-Ghosh method to extract shadow observables like area and oblateness from photon orbit analysis, linking theoretical predictions with EHT measurements.
• The study shows that holonomy corrections yield closed shadow rings even in horizonless geometries, supporting loop quantum gravity as a viable alternative in strong-field regimes.

Loop Quantum Gravity Signatures in Black Hole Shadows: Testing via EHT Observations of M87* and Sgr A* (2605.28871)

Background and Motivation

The quest to probe quantum gravity in astrophysically relevant settings is driven by the breakdown of classical General Relativity (GR) at curvature singularities, where quantum corrections are expected to become significant. Loop Quantum Gravity (LQG) provides a non-perturbative, background-independent quantization scheme of spacetime, in which geometric operators acquire discrete spectra, regularizing otherwise divergent curvature invariants. The most prominent feature in LQG is the replacement of classical curvature with holonomy corrections, parameterized through $SU(2)$ variables, leading to effective metrics that resolve singularities with non-trivial structure near the core.

Recent Event Horizon Telescope (EHT) observations have delivered horizon-scale images of two supermassive black holes (SMBHs): M87* and Sgr A*. These observations permit direct testing of strong-field gravity and the search for quantum gravitational imprints in black hole shadow morphology. Classical GR predicts the Kerr metric for rotating black holes, characterized essentially by mass $M$ and spin $a$. LQG-inspired metrics—including holonomy-corrected black holes—introduce an additional quantum correction parameter $b$, fundamentally altering the spacetime structure in the strong-field regime.

This paper develops the rotating holonomy-corrected black hole (RHCBH) metric through a modified Newman-Janis algorithm, analyzes its horizon structure and photon regions, and undertakes a systematic comparison of shadow observables with EHT measurements to constrain the quantum parameter $b$ and the spin $a$.

RHCBH Geometry and Horizon Structure

The RHCBH metric, derived via Azreg-Aïnou's non-complexification extension of the Newman-Janis algorithm, generalizes the Kerr metric by incorporating the quantum correction parameter $b$. The seed metric is a holonomy-corrected Schwarzschild solution, characterized by a wormhole-like structure and a finite Kretschmann scalar. The RHCBH metric preserves regularity in the central region, with the effective mass function and horizon structure altered as:

$\Delta(r) = r^2 - (2M + b) r + a^2 + 2Mb$

Depending on $(a, b)$, $\Delta(r) = 0$ yields either two horizons, one degenerate horizon (extremal), or no real roots (horizonless compact object). The physically admissible regions are mapped in $M$0 space, with extremal boundaries at $M$1. When $M$2 exceeds a threshold, the spacetime transitions to a regular, horizonless geometry, unlike Kerr naked singularities where curvature diverges.

Photon Dynamics and Shadow Morphology

Photon motion is analyzed via the Hamilton-Jacobi formalism, exposing three integrals of motion: energy, axial angular momentum, and the Carter constant. The effective radial potential defines unstable spherical photon orbits, demarcating the shadow boundary for a distant observer. Critical impact parameters $M$3 are analytically extracted, and their dependence on $M$4 and $M$5 is traced.

Key findings:

• Quantum corrections ($M$6) increase shadow radius: For fixed spin, the prograde photon orbit shifts outward with increasing $M$7, the retrograde orbit remains at $M$8. The overall shadow exhibits larger spatial extent, corresponding to a weaker effective gravitational field near the core.
• Closed shadow rings in horizonless RHCBHs: Unlike Kerr naked singularities, which yield arc-shaped open shadows due to horizon absence, RHCBHs can exhibit complete, closed shadow boundaries for $M$9 in the range $a$0. Closure is dictated primarily by the existence of unstable photon orbits, not the horizon per se, challenging standard interpretations based solely on shadow morphology.

Shadow Parameter Estimation: Kumar-Ghosh Observables

Parameter extraction departs from traditional circularity-based methods which fail in highly distorted or non-Kerr metrics. The Kumar-Ghosh method is employed, utilizing shadow area $a$1 and oblateness $a$2—both functions of $a$3—where intersection points of constant $a$4 and $a$5 contours in $a$6 space uniquely determine the physical parameters.

This approach resolves parameter degeneracy and is robust against shadow deformations arising in quantum or regular metrics, in particular for RHCBHs with potentially asymmetric shadow profiles.

EHT Constraints on RHCBH Parameters

Angular diameter bounds from EHT for M87* ($a$7) and Sgr A* ($a$8) are mapped onto the RHCBH parameter space. The Schwarzschild deviation parameter $a$9, defined as the fractional difference in angular shadow diameter relative to a Schwarzschild black hole, is also considered ($b$0, $b$1 for Keck, $b$2 for VLTI).

Set of constraints:

• M87* observations:
  • At $b$3, $b$4 (for $b$5), $b$6 (for $b$7).
  • At $b$8, $b$9 ($b$0), $b$1 ($b$2).
• Sgr A* observations:
  • At $b$3, $b$4 ($b$5), $b$6 ($b$7).
  • At $b$8, $b$9 ($a$0), $a$1 ($a$2).

These bounds validate that nonzero holonomy corrections ($a$3) are completely compatible with current EHT data, meaning RHCBH metrics are observationally viable alternatives to Kerr in the strong-gravity regime.

Comparative Analysis with Other Rotating Black Hole Models

The RHCBH parameter constraints are compared to those derived for other non-Kerr or regular spacetimes, including rotating quantum-corrected black holes, LQG-inspired models, bumblebee gravity, hairy Kiselev metrics, Bardeen, Hayward, Ghosh, and Simpson-Visser black holes.

• EHT shadow observables are consistent with all these models for a wide range of deviation parameters.
• Structural differences (linear vs. quadratic/exponential dependence on deviation parameters) are not yet distinguishable at current observational precision.
• Simpson-Visser black holes exhibit shadow structure independent of the deviation parameter $a$4, demonstrating non-uniqueness in shadow morphology among different regular metrics.

Practical and Theoretical Implications

The presence of quantum-corrected regular geometries consistent with EHT shadow observations confirms that classical GR is not strictly required in the strong-field regime for SMBHs. RHCBHs and other alternatives remain viable; sharper EHT images and future ngEHT arrays will be necessary to impose tighter constraints and distinguish between quantum modifications and classical metrics.

Closed shadow rings need not guarantee event horizon existence—the essential criterion is the existence of unstable photon orbits. This has important implications for interpreting high-resolution shadow data, especially in distinguishing horizonless regular spacetimes from naked singularities.

Future research directions include incorporating realistic accretion flow models, examining gravitational wave signatures (ringdown and echo phenomenology), and testing charged extensions of RHCBHs.

Conclusion

This comprehensive analysis demonstrates that rotating holonomy-corrected black holes from LQG, characterized by spin parameter $a$5 and quantum parameter $a$6, can produce shadow structures compatible with EHT observations of M87* and Sgr A*, yielding closed photon rings even in horizonless geometries. Parameter estimation via the Kumar-Ghosh method robustly constrains both $a$7 and $a$8. Comparative benchmarking against other quantum and regular metrics underscores current observational degeneracy. There is no evidence against nonzero quantum corrections at present EHT angular resolutions, and future, higher-precision measurements will be essential for explicit quantum gravity tests in astrophysical black hole environments.

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Reference:

"Testing loop quantum gravity through EHT observations of M87* and Sgr A* using rotating holonomy-corrected black holes" (2605.28871)