Vanessa Hahn (UP)
Oliver Lindblad Petersen
In this talk, we consider the Cauchy problem of the linearised Einstein equation on smooth globally hyperbolic spacetimes, satisfying the non-linear Einstein equation. Given smooth or distributional initial data (of arbitrary Sobolev regularity) specified on a spacelike Cauchy hypersurface, we show that there is a globally defined solution, which is unique up to gauge. Hence the solutions, modulo gauge, are in one-to-one correspondence with the initial data, modulo gauge producing initial data. If the Cauchy hypersurface is closed, this correspondence is actually an isomorphism of topological vector spaces. Therefore, in this sense, the Cauchy problem of the linearised Einstein equation is well posed.