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The past 10 years have seen remarkable progress in our capability of analyzing reflection features in the X-ray spectra of accreting black holes. Today X-ray reflection spectroscopy is a mature technique and a powerful tool for studying the accretion process around black holes, measuring black hole spins, and testing Einstein's theory of General Relativity in the strong field regime. However, current reflection models still rely on a number of simplifications and caution is necessary when we derive very precise measurements. In this paper, we study the impact of the returning radiation on our capability of measuring the properties of black holes using X-ray reflection spectroscopy, and in particular on our capability of testing the Kerr black hole hypothesis. While the returning radiation alters the reflection spectrum of the disk, from the analysis of our simulations we find that models without returning radiation can normally recover well the correct black hole spin parameters and can test the Kerr metric. [ABSTRACT FROM AUTHOR]

The optical properties of rotating black holes in Kaluza–Klein theory described by the total mass, spin, and electric and magnetic charges are investigated in detail. Using a developed general relativistic ray-tracing code to calculate the motion of photons, shadows of Kaluza–Klein black holes are generated. The properties of the shadow and the light deflection angle around these black holes are also studied in order to put constraints on the parameters of Kaluza–Klein black holes using M87* shadow observations. The possibility of imposing constraints on Kaluza–Klein black holes using shadow observations is investigated. Moreover, we find that small charges (electric and magnetic) of the black hole can meet these constraints. We conclude that with the current precision of the M87* black hole shadow image observation by the EHT collaboration, the shadow observations of Kaluza–Klein black holes are indistinguishable from that of the Kerr black hole. Much better observational accuracy than the current capabilities of the EHT collaboration are required in order to place verified constraints on the parameters of modified theories of gravity in the strong field regime. [ABSTRACT FROM AUTHOR]