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Nonlinear solutions for initial data in the vacuum Einstein equations in plane symmetry
Phys. Rev. D 39, 2155 – Published 15 April, 1989
DOI: https://doi.org/10.1103/PhysRevD.39.2155
Abstract
We present a study of the parameter space of solutions for initial data in the plane-symmetric vacuum Einstein equations. We use the York splitting into free and constrainted variables to find analytic solutions to the momentum and Hamiltonian constraints to first and second perturbative orders. We construct a numerical code to solve the equations in the full nonperturbative regime and present extensive tests to verify its accuracy. We parametrize the solution space by the amplitude of waves in the free data and present examples in several cases of interest. These results clearly show the differences among solutions to the linear, weakly nonlinear (second-order), and fully nonlinear equations.
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