  We introduce a new wave formulation for the relativistic Euler equations with
vacuum boundary conditions that consists of a system of non-linear wave
equations in divergence form with a combination of acoustic and Dirichlet
boundary conditions. We show that solutions of our new wave formulation
determine solutions of the relativistic Euler equations that satisfy the vacuum
boundary conditions provided the initial data is chosen to make a specific set
of constraints vanish on the initial hypersurface. Moreover, we prove that
these constraints propagate. This article is the first step of a two step
strategy to establish the local-in-time existence and uniqueness of solutions
to the relativistic Euler equations representing dynamical liquid bodies in
vacuum.
