On the efficiency of the Blandford-Znajek mechanism for low angular
  momentum relativistic accretion
  Blandford-Znajek (BZ) mechanism has usually been studied in the literature
for accretion with considerably high angular momentum leading either to the
formation of a cold Keplerian disc, or a hot and geometrically thick
sub-Keplerian flow as described within the framework of ADAF/RIAF. However, in
nearby elliptical galaxies, as well as for our own Galactic centre, accretion
with very low angular momentum is prevalent. Such quasi-spherical strongly
sub-Keplerian accretion has complex dynamical features and can accommodate
stationary shocks. In this letter, we present our calculation for the maximum
efficiency obtainable through the BZ mechanism for complete general
relativistic weakly rotating axisymmetric flow in the Kerr metric. Both shocked
and shock free flow has been studied in detail for rotating and counter
rotating accretion. Such study has never been done in the literature before. We
find that the energy extraction efficiency is low, about 0.1%, and increases by
a factor 15 if the ram pressure is included. Such an efficiency is still much
higher than the radiative efficiency of such optically thin flows. For BZ
mechanism, shocked flow produces higher efficiency than the shock free
solutions and retrograde flow provides a slightly larger value of the
efficiency than that for the prograde flow.
