Linearization stability of the Einstein equations

Fischer, A. E. and J. E. Marsden

Bull. Amer. Math. Soc., 79, (1973), 997-1003

Abstract:

An important problem in general relativity is the question of whether or not a solution of the linearized Einstein field equations (relative to a given background solution) actually approximates to first order a curve of exact solutions to the nonlinear equations. Here we announce that under certain geometrical conditions on the background solution the problem can be answered affirmatively; however, in certain exceptional cases the answer may be negative. In the affirmitive case we shall say that the background metric is linearization-stable.