Review the possible advective disk structures around a black hole with two-type gas inflows

We studied the general advective accretion solutions around the Kerr black hole (BH) with investigating two types of inflow gases at the outer accretion boundary (AB). We classified these two types of gases as a \cm and a \hm inflow gas at the outer AB on the basis of their temperatures and solutions. We found that the \hm gas is more efficient for angular momentum transportation around the outer AB than the \cm gas. The \hm gas can give global multiple \cite[popular as shock solution][]{c89} or single sonic point solutions and the \cm can give smooth global solution \cite[popular as ADAF][]{ny94} or two sonic point solutions. These solutions also represented on a plane of energy and angular momentum ($\be-L_0$) parameter space. Theoretically for the first time, we explored the relation between the nature of accretion solutions with the nature of initial accreting gas at the AB with detail computational and possible physical analysis. We also found that the surface density of the flow is highly affected with changing of the temperature at the AB, which can alter the radiative emissivities of the flow. The flow variables of various advective solutions also compared. On the basis of those results, we plotted some inner disk structures around the BHs. Doing so, we conjectured about the persistent/transient nature of spectral states, soft-excess and time scales of variabilities around the black hole $X-$ ray binaries (BXBs) and active galactic nuclei (AGNs).