Using the magnetofluid unification framework, we show that the accretion disk plasma (embedded in the background geometry of a black hole) can relax to a class of states known as the Beltrami-Bernoulli (BB) equilibria. Modeling the disk plasma as a Hall magnetohydrodynamics (MHD) system, we find that the space-time curvature can significantly alter the magnetic (velocity) decay rates as we move away from the compact object; the velocity profiles in BB states, for example, deviate substantially from the predicted corresponding geodesic velocity profiles. These departures imply a rich interplay of plasma dynamics and general relativity revealed by examining the corresponding Bernoulli condition representing "homogeneity" of total energy. The relaxed states have their origin in the constraints provided by the two helicity invariants of Hall MHD. These helicities conspire to introduce an oscillatory length scale into the system that is strongly influenced by relativistic and thermal effects. © 2015 American Physical Society.