  Short-time existence for the Einstein-Euler and the vacuum Einstein equations
is proven using a Friedrich inspired formulation due to Choquet-Bruhat and
York, where the system is cast into a symmetric hyperbolic form and the Riemann
tensor is treated as one of the fundamental unknowns of the problem. The
reduced system of Choquet-Bruhat and York, along with the preservation of the
gauge, is shown to imply the full Einstein equations.
