Viscous shear in general-relativistic astrophysical flows

Abstract

Introducing the concept of general co-moving frames (gcmf) in [4] we have argued that it may become useful in a number of hydrodynamical and mhd applications. In [5] using thegcmf technique we have constructed a fully covariant, general-relativistic theory of strongly magnetized collisionless plasma. The approach proved itself to be highly convenient-it allowed us to find new equations of state for such a medium. In the present paper we have considered viscous shear in generalrelativistic astrophysical flows as an another example of the effective usage of orthonormal tetrads method. Namely, we have specified general corotating frames (gcrf)-subclass ofgcmf corresponding to the flows being in purely rotational motion. By means of gcrf we have been able to find expressions for nonzero components of shear tensor and turbulent viscosity tensor for the innermost region of a black hole accretion disc. We think that the method may be useful when considering analogous problems with astrophysical flows of more complicated geometry and/or dynamics. In particular, the method may become efficient for jets in active galactic nuclei (agn) and quasars [13], general-relativistic winds of compact objects [14] and the innermost regions of candidates for galactic black hole accretion discs [15]. To be sure, in some of these problems we have to use a more general set ofgcmf instead ofgcrf. Such problems, however, are beyond the scope of this paper, where we have only outlined the main background of the method and demonstrated its productivity in a simple case of quasi-keplerian accretion flow in a general-relativistic standard accretion disc.