Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk

Abstract: Latest advances in effective quantum gravity propose a quantum-corrected black hole solution that avoids Cauchy horizons. In this paper, we study the image of the black hole and explore the influence of the quantum parameter $\zeta$ on its image. First, we investigate the influence of $\zeta$ on the event horizon, photon sphere, critical impact parameter, and innermost stable circular orbit associated with the black hole. We find that all these quantities exhibit an increase with increasing $\zeta$. Meanwhile, we analyze the allowed range of $\zeta$ from both theoretical and observational perspectives. We then derive the photon trajectory equation and analyze briefly the behavior of the trajectories. A detailed analysis shows that as $\zeta$ increases, the photon trajectories near the event horizon undergo modifications. Finally, by plotting the optical appearance of the black hole under three emission models, we find that as $\zeta$ increases, the quantum-corrected black hole exhibits a larger shadow, along with a brightening of the bright rings and a reduction in the spacing between them near the critical impact parameter. Therefore, we can distinguish the quantum-corrected black hole from the Schwarzschild one by its unique optical appearance.