Stability by linearization of Einstein’s equation at Minkowski’s initial metric

© 2010, Birkhäuser, Springer Basel AG. Let us recall that in Chapter III we studied the case of a gravitational field created by matter with a small stress-energy tensor, and where we saw (by linearization at Minkowski’s initial metric) how in this case Einstein’s equation was related to the wave equation. However, this naturally raises the question of whether or not it is admissible to linearize Einstein’s equation at Minkowski’s initial metric. In other words, whether or not Einstein’s equation is stable by linearization at Minkowski’s initial metric.