We study the application of Lorentz kinematic transformations deformed by critical velocity to a continuity equation. This generates a source structure for the continuity equation that is indistinguishable from a Nernst–Planck equation. In this case, the fluid flow is the source of excited states. This makes the fluid a type of self-source, where the flow is a force that compensates for its crystallization into excited states. Therefore, we can understand that the kinematic transformation adds a stress term to the fluid dynamics, which can be understood as a sort of dark energy.

We studied the effects of the currents that arise. Specifically, the dissipative and convective currents, which play a role of self-induction and mutual induction, are capable of generating local phase transitions in the fluid.

This construction is a step toward building a theory of gravity based on a theory of two self-interacting fluids. In future work, we will clarify the role of vorticity, include viscosity effects, and relate this to Helmholtz–Hodge decomposition. We will also clarify the dynamic role of critical velocity as a fundamental state and its effect on the causal structure of the fluid, in addition to investigating a possible condition of non-integrability, which should severely affect the construction of the causal structure.