  Matter makes a transition from non-relativistic to relativistic regime, as it
falls onto a black hole. We employ a relativistic equation of state,
abbreviated as RC, to study multi-species fluid flow around black holes. We
show that pair-plasma fluid around a black hole is thermally not relativistic.
In order to make it relativistic, a finite baryon loading is necessary. As a
consequence of this, pair-plasma flow do not suffer centrifugal pressure driven
shock in accretion. However, fluid with finite baryon content may undergo shock
transition.
