Shear tensor and dynamics of relativistic accretion disks around rotating black holes

TL;DR

This paper presents a fully relativistic analysis of shear tensors in steady-state accretion disks around Kerr black holes, introducing a new method to compute shear components in various frames and deriving analytical solutions.

Contribution

It introduces a novel method for calculating shear tensors in different frames and shows that two components are nonzero in the fluid rest frame, unlike previous assumptions.

Findings

Two shear tensor components are nonzero in the FRF.

Analytical solutions for velocity and density are derived.

The method is compatible with transonic solutions and causal viscosity.

Abstract

In this paper we solve the hydrodynamical equations of optically thin, steady state accretion disks around Kerr black holes. Here, fully general relativistic equations are used. We use a new method to calculate the shear tensor in the LNRF (Locally Non-Rotating Frame), BLF (Boyer-Lindquist Frame) and FRF (Fluid Rest Frame). We show that two components of shear tensor in the FRF are nonzero (in previous works only one nonzero component was assumed). We can use these tensors in usual transonic solutions and usual causal viscosity, but we derive solutions analytically by some simplifications. Then we can calculate the four velocity and density in all frames such as the LNRF, BLF and FRF.