Oliver Lindblad Petersen
In this talk we discuss the well-posedness of the Cauchy problem for the linearised Einstein vacuum equation on arbitrary globally hyperbolic vacuum spacetimes. The solution space of the linearised Einstein equation (graviational waves) modulo gauge solutions is shown to be in one-to-one correspondence with initial data modulo gauge. This correspondence is given by an isomorphism of topological vector spaces. One concludes global existence, uniqueness and continuous dependence on initial data. This extends our results presented in an earlier research talk, where the special case of spatially compact spacetimes was considered.
The statement is shown for smooth and distributional initial data of arbitrary Sobolev regularity. As an application, we give examples of spacetimes with arbitrarily irregular (non-gauge) solutions to the linearised Einstein equation.