Calculation of the relativistic Bulk Viscosity, Shear Viscosity and Shear-Stress Viscosity of Accretion Disks around the Rotating Black Holes

TL;DR

This paper calculates the relativistic bulk, shear, and shear-stress viscosities of accretion disks around rotating black holes, providing detailed tensor components and analyzing their behavior in relativistic frames.

Contribution

It introduces a comprehensive calculation of relativistic viscosity tensors in accretion disks around rotating black holes, including their components and behavior in different frames.

Findings

Derived all non-zero components of the viscosity tensors in the equatorial plane.

Presented figures illustrating the behavior of tensor components for various states.

Highlighted the significance of relativistic bulk viscosity in black hole accretion disks.

Abstract

In this paper we study the relativistic bulk tensor, shear tensor and the shear stress viscosity of the relativistic accretion disks around the rotating black holes. we calculate all non-zero components of the bulk tensor, shear tensor and shear stress viscosity in the equatorial plan in the BLF. We obtain the relations of the relativistic bulk tensor, shear tensor and shear stress viscosity in the terms of components of four velocity and derivatives, Christoffel symbols and metric components. To see the behaviorr of the components of relativistic bulk tensor, shear tensor and shear stress viscosity, we introduce a radial form for the radial component of the four velocity in the LNRF then all components of the bulk tensor, shear tensor and shear stress viscosity are derived in BLF. Figures of non-zero components of the bulk tensor, shear tensor and shear stress viscosity are shown for some states. The importance and influence of the relativistic bulk viscosity in the accretion disks around the rotating black holes are studied in this paper.