  In almost all of plasma theories for astrophysical objects, we have assumed
the charge quasi-neutrality of unmagnetized plasmas in global scales. This
assumption has been justified because if there is a charged plasma, it induces
electric field which attracts the opposite charge, and this opposite charge
reduces the charge separation. Here, we report a newly discovered instability
which causes a charge separation in a rotating plasma inside of an innermost
stable circular orbit (ISCO) around a black hole. The growth rate of the
instability is smaller than that of the disk instability even in the unstable
disk region and is forbidden in the stable disk region outside of the ISCO.
However, this growth rate becomes comparable to that of the disk instability
when the plasma density is much lower than a critical density inside of the
ISCO. In such case, the charge separation instability would become apparent and
cause the charged accretion into the black hole, thus charge the hole up.
