  We present new JVLA and VLBA observations tracing the HI in the central
region of 3C84 (Perseus A). This radio source is hosted by the bright cluster
galaxy NGC 1275 in the centre of the iconic Perseus cluster. With the JVLA, we
detected broad (FWHM~500 km/s) HI absorption at arcsecond resolution (~300 pc)
centred at the systemic velocity of NGC 1275 against the bright radio
continuum, suggesting that the detected gas is very close to the supermassive
black hole (SMBH). However, we did not detect any absorption in the
higher-resolution VLBA data against the parsec-scale radio core and jet. Based
on a comparison of the properties of the HI absorption with those of the
molecular circum-nuclear disc (CND) known to be present in NGC 1275, we argue
that the HI seen in absorption arises from HI in this fast-rotating CND, and
that neutral atomic hydrogen is present as close as ~20 pc from the SMBH. The
radio continuum providing the background for absorption arises from non-thermal
synchrotron emission from the star formation activity in the CND, whose
presence has been reported by earlier VLBA studies. We did not detect any
signature that the HI gas is affected by an interaction with the radio jet.
Thus, at this stage of the evolution of the source, the impact of the radio jet
on the gas in NGC 1275 mainly creates cavities on much larger galaxy scales.
Overall, the properties of the CND in Perseus A present strong similarities
with Mrk 231, suggesting that, unlike often assumed, HI absorption can arise
against the radio emission from star formation in a CND. With the JVLA, we
serendipitously detected a new, faint absorbing system that is redshifted by
~2660 km/s, in addition to the already known high-velocity absorption system
that is redshifted 2850 km/s with respect to NGC 1275. We identify this new
system as gas that is stripped from a foreground galaxy falling into the
Perseus cluster.
