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. This paper studies the images of this black hole when illuminated by a static thin accretion disk and explores the effect of the quantum parameter ζ on its appearance. First, we investigate the influence of ζ 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 ζ. Meanwhile, we also use observational data from M87* and Sgr A* to impose constraints on ζ and compare the results with the theoretical constraint. Our analysis reveals that the observational constraint from Sgr A* is stronger than the theoretical one. We then derive the photon trajectory equation and analyze briefly the behavior of the trajectories. A detailed analysis shows that as ζ increases, the trajectories of photons undergo slight modifications when approaching the event horizon. Finally, by plotting the black hole's optical appearance under three emission models, we find that as ζ increases, the quantum-corrected black hole exhibits a larger shadow, along with narrower lensed and photon rings and reduced spacing between them. Furthermore, we also implement Johnson's unbound distribution to simulate the image of the quantum-corrected black hole under large quantum parameters and reach the same conclusion. This work validates the rationality of this black hole solution through observational data, and provides its unique optical signatures that can serve as a promising avenue for probing quantum gravity effects near black holes.