Weak gravitational lensing by Kerr-MOG black hole and Gauss–Bonnet theorem

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The deflection angle of Kerr-MOG black holes is studied for different values of the parameter in modified gravity (MOG). To this end, we employ the Gauss-Bonnet theorem, which was first studied by Gibbons and Werner and then extended by Ono, Ishihara and Asada, who use a generalized optical metric where the deflection of light for an observer and source at finite distance. By using this method, we study the weak gravitational lensing by Kerr-MOG black hole. Our computations show that with an increase in the MOG parameter ($\alpha$), the deflection angle becomes significantly larger than that of Kerr black hole. The results obtained show that MOG effect could be taken into account in the gravitational lensing experiments.