Particle scattering by a test fluid on a Schwarzschild spacetime: the equation of state matters

The motion of a massive test particle in a Schwarzschild spacetime surrounded by a
perfect fluid with equation of state $p_0= w \rho_0$ is investigated.
Deviations from geodesic motion are analyzed as a function of the parameter
$w$, ranging from $w=1$ which corresponds to the case of massive free scalar fields, down into
the so-called ``phantom" energy, with $w<-1$.
It is found that the interaction with the fluid leads to capture (escape) of the particle trajectory in the case $1+w>0$ ($<0$), respectively.
Based on this result, it is argued that inspection of the trajectories of test particles in the vicinity
of a Schwarzschild black hole with matter around may offer a new means of gaining insights into the nature of cosmic matter.