Analyzing the influence of geometrical deformation on photon sphere and shadow radius: A new analytical approach-stationary, and axisymmetric spacetime

Black hole shadows and photon spheres offer valuable tools for investigating black hole properties. Recent observations by the Event Horizon Telescope Collaboration have confirmed the existence of rotating black holes. Black hole parameters influence the observed shadow size. This paper aims to extend the work in [V. Vertogradov and A. Övgün, Analyzing the influence of geometrical deformation on photon sphere and shadow radius: A new analytical approach — spherically symmetric spacetimes, Phys. Dark Univ. 45 (2024) 101541] and explores the impact of geometrical deformations on black hole shadow size using gravitational decoupling to an axially symmetric spacetime. We find that the results are more complex than the spherically symmetric case. We compare shadows in the well-known models with those of a Kerr black hole. Our approach suggests that the influence of an accretion disc on the observed shadow shape can be accurately described despite negligible impact on the black hole geometry itself.