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In this paper, we investigate the optical properties of a charged black hole with scalar hair (CSH) within the context of four-dimensional Einstein–Maxwell–Dilaton gravity. To achieve this, we consider three distinct toy models of thin accretion disks. The presence of dilaton coupling allows us to express both the solutions of CSH and the Reissner–Nordström (RN) black hole in terms of their mass (M) and charge (Q). Our findings reveal differences in the effective potentials V eff , photon sphere radii r ph , and innermost stable circular orbit r isco between the CSH and RN black hole cases, which become increasingly pronounced as the charge parameter Q increases. However, no noticeable distinctions are observed concerning the critical impact parameter b ph . When the ratio of the photon ring band and the lensed ring band exceeds 0.1, it may suggest the presence of a charged black hole with scalar hair. Furthermore, our results underscore the significant influence of the charge parameter Q on the brightness distributions of the direct, lensed ring, and photon ring for three standard emission functions. These findings emphasize the potential for distinguishing between CSH and RN black holes through an analysis of direct intensity and peak brightness in specific accretion disk models. [ABSTRACT FROM AUTHOR]

We investigate two different kinds of modified Schwarzschild black holes: A regularized Schwarzschild black hole and a quantum deformed Schwarzschild black hole. We study the geodesics and geodesic congruences in these two modified Schwarzschild black holes. In particular, we calculate the expansion of radial timelike and null geodesic congruences. Based on these results, we discuss some similarities and differences between these two kinds of modified Schwarzschild black holes. [ABSTRACT FROM AUTHOR]