Abstract: Let (M, g) be a 4-dimensional Lorentzian manifold. Then the empty space Einstein Field Equations are equivalent to the vanishing of the Ricci curvature of the metric g, which essentially leads to a system of second-order partial differential equations(PDEs) in some local coordinates. This system of PDEs can be reduced to a system of quasilinear second-order hyperbolic system under some "mild" conditions.
In this talk, we plan to present a theorem about the existence and uniqueness of the local solution to such a system of quasilinear second-order PDEs. Since we will present a coordinate-based proof, no prior knowledge of differential geometry is needed. This talk is expected to be self-contained.
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