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Abstract We study thin accretion disks in the gravitational field of a class of rotating regular black holes. Our objective is to determine the key parameters governing these accretion disks: the radius of the innermost stable circular orbit $$(r_{\textrm{ISCO}})$$ ( r ISCO ) and the efficiency $$(\eta )$$ ( η ) of the accretion disk in converting matter into radiation. We employ a simplified model to describe the disk’s radiative flux, and differential and spectral luminosity. Subsequently, we compare our findings with the expectations from accretion disks around Kerr black holes. Notably, our calculations reveal that both the luminosity of the accretion disk and its efficiency are greater when considering the geometry of rotating regular black holes, particularly for fixed and small values of the spin parameter (j), in contrast to the predictions obtained using the Kerr metric for a black hole of the same mass. These results offer intriguing insights into the behavior of astrophysical black holes.

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields.