  The aim of this paper is to clarify the distinction between homoclinic and
standard (global) Bondi-type accretion solutions in the Schwarzschild-anti-de
Sitter spacetime. The homoclinic solutions have recently been discovered
numerically for polytropic equations of state. Here I show that they exist also
for certain isothermal (linear) equations of state, and an analytic solution of
this type is obtained. It is argued that the existence of such solutions is
generic, although for sufficiently relativistic matter models (photon gas,
ultra-hard equation of state) there exist global solutions that can be
continued to infinity, similarly to standard Michel's solutions in the
Schwarzschild spacetime. In contrast to that global solutions should not exist
for matter models with a non-vanishing rest-mass component, and this is
demonstrated for polytropes. For homoclinic isothermal solutions I derive an
upper bound on the mass of the black hole for which stationary transonic
accretion is allowed.

General Relativity and Quantum Cosmology