Consistency of the mass variation formula for black holes accreting
  cosmological fluids
  We address the spherical accretion of generic fluids onto black holes. We
show that, if the black hole metric satisfies certain conditions, in the
presence of a test fluid it is possible to derive a fully relativistic
prescription for the black hole mass variation. Although the resulting equation
may seem obvious due to a form of it appearing as a step in the derivation of
the Schwarzschild metric, this geometrical argument is necessary to fix the
added degree of freedom one gets for allowing the mass to vary with time. This
result has applications on cosmological accretion models and provides a
derivation from first principles to serve as a base to the accretion equations
already in use in the literature.
