Influence of Quantum Correction on Kerr Black Hole in Effective Loop Quantum Gravity via Shadows and EHT Results (2501.01308v3)

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 $\gamma$. 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 $\gamma$. 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.