The inverse spectral method for colliding gravitational waves
The authors use the inverse spectral method to solve the boundary value problem associated with the partial differential equations that describe the interaction of two plane gravitational waves in flat background after their collisions. This equation, which is particular exact reduction of the vacuum Einstein equations, is integrable, i.e., it possesses a Lax pair formulation. The above equation and its linearized version are considered by using simultaneous spectral analysis of the Lax pair and it is shown that the linear problem can be reduced to a scalar Riemann-Hilbert problem which can be solved in closed form. The nonlinear problem reduces to a \(2\times 2\) matrix Riemann-Hilbert problem, which is integrable under certain conditions.
scientific article; zbMATH DE number 1334575