The inverse spectral method for colliding gravitational waves
type: Item
instance of: scholarly article
title: The inverse spectral method for colliding gravitational waves
zbMATH Open document ID: 0937.37050
DOI: 10.1023/A:1009870125810
author: V. Pereyra
published in: Mathematical Physics, Analysis and Geometry
publication date: 2000-06-08T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37K15
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 83C35
zbMATH DE Number: 1334575
zbMATH Keywords: colliding gravitational waves
zbMATH Keywords: Hilbert problem
zbMATH Keywords: inverse spectral method
zbMATH Keywords: Einstein equations
zbMATH Keywords: Lax pair
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1334575