Correlation Of The Black Hole Spin With The Inner Edge Radius Of An Accretion Disc

A constraint to black hole (BH) accretion has previously been derived for the inner edge fixed at the innermost stable circular orbit (ISCO) and the innermost bound circular orbit (IBCO). This constraint is referred to as the mass-radius (MR) relation in this study, and the validity of the MR relation is discussed for different cases. It is shown that the product of the BH mass and the inner edge radius decreases monotonically in the accretion process for the inner edge located between IBCO and ISCO. In addition, we discuss the validity of the MR relation by considering the magnetic coupling (MC) effects of a Kerr BH with its surrounding disc. Although theoretically the product of the BH mass and the radius of ISCO increases (decreases) with time for a BH spin greater (less) than some critical value in the MC process, this relation is approximately valid for an Eddington accretion rate persisting for a rather long time, such as more than 106years. This paper is organized as follow. Firstly, we briefly introduce the basic theory of black hole and BZMC coexistence model, and introduce the change of inner edge of accretion disc. The evolution of the inner edge of accretion disc is one of the most important conceptions in understanding MR relation. Secondly, we discuss the validity of the MR relation in accretion process with the MC effects. Finally, we discuss the application of MR relation in astrophysics, which is focused on black hole binaries and radio dichotomy of quasars.