A Study of thin relativistic viscose accretion disk around a distorted kerr black hole (DKB)

In this paper, we analyze a thin disk around the distorted Kerr black hole (DKB) within the framework of general relativity using an axisymmetric solution of the Einstein equations. We consider this accretion disk around the Kerr black hole in an external gravitational field up to the quadrupole moment and discuss the key aspects of black hole accretion disk theory. Our findings indicate that the presence of a quadrupole moment significantly influences the radiation emitted from the accretion disk. While the location of the innermost stable circular orbit (ISCO) remains largely unchanged, the magnitude of the radiation flux, as well as the shape, orientation, and energy distribution of the accretion disk, are affected. The direction of distortion of the event horizon determines whether the disk becomes more oblate or prolate, impacting observed variations in maximum height, position, and temperature. Furthermore, the quadrupole moment alters the geometry of the black hole's spacetime, which can influence the efficiency of energy extraction from the black hole's spin, an important factor in powering emissions from accretion disks. We obtain dynamical quantities around a distorted rotating black hole disk. Additionally, we examine how rotation influences the dynamics of the DKB. We also investigate the effects of varying the viscosity coefficient on the behavior of the DKB.