Constant Velocity Rotation Curves for Gravitating Systems in Hydrostatic Equilibrium

The familiar problem of a system having simple linear equation of state (EOS) is re-examined, revealing a new solution for both relativistic and non-relativistic systems that evolves smoothly from the origin to a single point of convergence. This leads to rotational velocity curves that closely match those for galaxies, and reduces to a universal rotation curve that can be fit to any observed rotation curve by making adjustments to two parameters that arise naturally in the theory. Flat rotation curves are therefore found to be a natural consequence of the balance between gravity and hydrostatic pressure for diffuse fluids in hydrostatic equilibrium, without presupposing the existence of dark matter. Additionally, for the relativistic case it is shown that systems with a linear EOS cannot collapse into black holes.