Modelling galaxy halos using dark matter with pressure

We investigate whether a dark matter with substantial amounts of pressure, comparable in magnitude to the energy density, could be a viable candidate for the constituent of dark matter halos. We find that galaxy halos models, consistent with observations of flat rotation curves, are possible for a variety of equations of state with anisotropic pressures. It turns out that the gravitational bending of light rays passing through such halos is very sensitive to the pressure. We propose that combined observations of rotation curves and gravitational lensing can be used to determine the equation of state of the dark matter. Alternatively, if the equation of state is known from other observations, rotation curves and gravitational lensing can together be used to test General Relativity on galaxy scales.