The general-relativistic magnetohydrodynamical (GRMHD) formulation for black
hole-powered jets naturally gives rise to a stagnation surface, wherefrom
inflows and outflows along magnetic field lines that thread the black hole
event horizon originate. We derive a conservative formulation for the transport
of energetic electrons which are initially injected at the stagnation surface
and subsequently transported along flow streamlines. With this formulation the
energy spectra evolution of the electrons along the flow in the presence of
radiative and adiabatic cooling is determined. For flows regulated by
synchrotron radiative losses and adiabatic cooling, the effective radio
emission region is found to be finite, and geometrically it is more extended
along the jet central axis. Moreover, the emission from regions adjacent to the
stagnation surface is expected to be the most luminous as this is where the
freshly injected energetic electrons concentrate. An observable stagnation
surface is thus a strong prediction of the GRMHD jet model with the prescribed
non-thermal electron injection. Future millimeter/sub-millimeter (mm/sub-mm)
very-long-baseline interferometric (VLBI) observations of supermassive black
hole candidates, such as the one at the center of M87, can verify this GRMHD
jet model and its associated non-thermal electron injection mechanism.Comment: 19 pages, 12 figure; accepted for publication in Ap
