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=wρ 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.