  We argue that combined observations of galaxy rotation curves and
gravitational lensing not only allow the deduction of a galaxy's mass profile,
but also yield information about the pressure in the galactic fluid. We
quantify this statement by enhancing the standard formalism for rotation curve
and lensing measurements to a first post-Newtonian approximation. This enhanced
formalism is compatible with currently employed and established data analysis
techniques, and can in principle be used to reinterpret existing data in a more
general context. The resulting density and pressure profiles from this new
approach can be used to constrain the equation of state of the galactic fluid,
and therefore might shed new light on the persistent question of the nature of
dark matter.
