!! CAUTION !! This is “MY QUESTION”. This can be in discord with standard view.
According to Wikipedia, Birkhoff’s theorem is explained as;
Birkhoff’s theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric.
As long as I know, all other textbooks and papers say the same.
But, even if there were a perfectly spherical symmetric supernova explosion, it must be observed spherically symmetric only by an observer who stays at the center of the supernova.
By an observer who stays outside the star, the explosion must be observed as it begins from the near side surface of the star and propagates to the far side after time delay of diameter of the star by speed of light. Gravity is also thought to propagate at the speed of light as light does. Therefore, for this observer, the center of the gravity of the supernova, I consider, must be observed to be approaching to him and gravity must be intensified.
Based on this “theorem”, it is said that gravitational wave only has shear wave, and there is no longitudinal gravitational wave. As long as I know, all textbooks and papers support this, too. But I think above-mentioned phenomena represents longitudinal gravitational wave.
Column by Mr. EMAN (Sorry, this is a Japanese page. But this is a common view.) whom I respect as my teacher without permission explains very carefully that gravitational wave is shear wave. My understanding about this column is not sufficient for talking decisively, but I am dubious about the very beginning of this theory. As most textbook do, gravity field is described with perturbation method in which metric of the field is presented as weak deviation from the flat background of Minkowski metric. I am afraid that already at this first point, finite propagation speed of the gravity seems to be out of consideration.