Influence of Quantum Correction on Kerr Black Hole in Effective Loop Quantum Gravity via Shadows and EHT Results

TL;DR

The paper investigates how effective Loop Quantum Gravity corrections, anchored by a fixed Barbero-Immirzi parameter $γ$, modify a rotating Kerr black hole and imprint on its shadow. By formulating a quantum-corrected Kerr metric with $\Delta(r)=\Delta_{Kerr}(r)+\frac{\alpha M^2}{r^2}$ and using Hamilton–Jacobi separability, it analyzes unstable null orbits, derives a theorem showing quantum corrections shrink these orbits, and computes shadow contours and celestial coordinates. Comparing predicted shadows to EHT data for M87* and Sgr A* reveals that M87* cannot be mimicked by the quantum-corrected Kerr at $1\sigma$, while Sgr A* can be mimicked within $1\sigma$, with LQG effects bringing the quantum-corrected case closer to the observed median; plasma further reduces shadow size and enhances sensitivity to the plasma model. The work constrains LQG-induced deviations via astrophysical shadows and highlights plasma as a significant modulator of the shadow, offering a pathway to test quantum gravity in strong-field regimes.

Abstract

Recently, a study on shadow of quantum corrected Schwarzschild black hole in loop quantum gravity appeared in [Ye et al., Phys. Lett. B 851, 138566, (2024)] assuming a fixed value of Barbero-Immirzi parameter $γ$. Following this approach, we considered its rotating counterpart being a quantum corrected Kerr black hole in effective loop quantum gravity and studied its deviation from Kerr black hole for a fixed value of $γ$. We proposed and proved a theorem describing the location of unstable circular null orbits for all such Kerr-like metrics. The deviation between the shadows of the Kerr and quantum corrected Kerr black holes has also been studied, and parameters are constrained by comparison with the EHT results for M87* and Sgr A* to precisely probe the quantity of deviation due to quantum correction. Lastly, we immersed the quantum corrected Kerr black hole in an inhomogeneous plasma and studied its impact on the shadow size. We found that the unstable null orbits for the quantum corrected Kerr black hole are always smaller than the unstable null orbits for Kerr black hole. The effect of Barbero-Immirzi parameter allows the quantum corrected Kerr black hole to mimic Sgr A* with a higher probability than the Kerr black hole. However, the quantum corrected Kerr black hole does not mimic M87*. The plasma reduces the size of the shadow of quantum corrected black hole, and the plasma parameter in the case II is more sensitive than that in case I.

Figures (5)

• Figure 1: Horizon structure of Kerr and quantum corrected Kerr BHs with respect to $a$ for $M=1$ and $\alpha\approx1.1663$.
• Figure 2: Behavior of effective potential and unstable null orbits for Kerr and quantum corrected Kerr BHs for different values of $a$ with $M=1$ and $\alpha\approx1.1663$.
• Figure 3: Behavior of shadows for Kerr and quantum corrected Kerr BHs for different values of $a$ with $M=1$ and $\alpha\approx1.1663$, visualized by an equatorial observer at radial infinity.
• Figure 4: Comparison of shadow angular diameter $\theta_\text{d}$ for quantum corrected Kerr BH (dashed red curve) and Kerr BH (solid black curves) with the EHT data for M87* (at inclination angle of $17^\circ$) and Sgr A* (at inclination angle of $45^\circ$) for the bounds on spin $a$ within 1-$\sigma$ intervals.
• Figure 5: Influence of $\omega_\text{c}$ in case I (upper panel) and case II (lower panel) on shadows of quantum corrected Kerr BH for a fixed value of $a$.