Nonlinear wave solutions to the planar vacuum Einstein equations

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Abstract
We use the 3+1 split of spacetime and the York splitting into free and constrained variables to set up initial data and solve the vacuum Einstein equations in plane symmetry. We present numerical solutions for free data in the form of traveling waves in both the linear and nonlinear regimes. No evidence of nonlinear wave propagation is found and we demonstrate that for our class of metrics the nonlinearity lies in the "Coulomb" or nonradiative components of the Riemann curvature tensor.