  It is likely that nearly all central galactic massive and supermassive black
holes are nonradiative: their accretion luminosities are orders of magnitude
below what can be explained by efficient black hole accretion within their
ambient environments. These objects, of which Sagittarius A* is the best-known
example, are also dilute (mildly collisional to highly collisionless) and
optically thin. In order for accretion to occur, magnetohydrodynamic
instabilities must develop that not only transport angular momentum, but also
gravitational energy generated through matter infall, outwards. A class of new
magnetohydrodynamical fluid instabilities -- the magnetoviscous-thermal
instability (MVTI) (Islam12) -- was found to transport angular momentum and
energy along magnetic field lines through large (fluid) viscosities and thermal
conductivities. This paper describes the collisionless and mildly collisional
analogue to the MVTI, the collisional magnetothermal instability (CMTI), that
similarly transports energy and angular momentum outwards, expected to be
important in describing the flow properties of hot, dilute, and radiatively
inefficient accretion flows around black holes. In this paper we derive a form
of the collisionless drift-kinetic equation appropriate for accretion physics.
We construct a local equilibrium for MHD stability analysis in this
differentially rotating disk. We then find and characterize specific
instabilities expected to be important in describing the flow properties of
hot, dilute, and radiatively inefficient accretion flows around black holes,
and show their qualitative similarities to instabilities derived using a fluid
formalism (Islam12). We conclude with further work needed in modeling this
class of accretion flow.
