Wellposedness of the Cauchy problem of the linearized Einstein-Klein-Gordon equations

02.07.2015, 16:15 Uhr  –  Neues Palais, Haus 9, Raum 2.06
Forschungsseminar Differentialgeometrie

Oliver Lindblad Petersen

We prove existence of a global solution to the linearized Einstein-Klein-Gordon equations, given initial data satisfying the linearized constraint equations. This solution is never unique, as one expects, recalling the non-linear case. The solution is, however, unique up a "linearized diffeomorphism". We thus do not have uniqueness of solution in the sense of linear wave equations and the solution can therefore not depend continuously on initial data in the usual sense. However, we conclude the talk by proving a statement that should be thought of as the continuous dependence of initial data.