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.