General Relativity at an interface

In this work a simple toy model for a free interface between bulk phases in space and time is presented, derived from the balance equations for extensive thermodynamic variables of Meinhold-Heerlein. In this case the free interface represents geodesics in the space-time, allowing the derivation of the Einstein's equations for gravitational fields. The effect of the balance equation is examined and a simple expression for cold dark matter is derived. The thermodynamically meaning of this model is also discussed.