Here we highlighted that there is a physical contradiction not only between the static and non-static versions of the de Sitter metric, but even between the old 1917 static interpretation and the present static interpretation.
Thus when there is no spacetime cross term, the two terms "non-stationary" and "non-static" become synonymous.
Obviously one cannot subscribe to both these views that the de Sitter universe is both, naturally, "static" and "non-static" simply because they are self-contradictory.
Here we highlight the conflicts between the static and non-static versions of the de-Sitter metric from a physical perspective.
In particular, the entire question of the static or non-static view is ascribed to the peculiarites of the coordinate transformations relating the two forms: and Historically, it was Lanczos11 who first pointed out that the static de Sitter metric can be given a non-static look by means of the above coordinate transformations.
But following the developments of GR, and in particular FRW cosmology, the de Sitter metric is believed to be naturally non-static, and just a special form of the non-static FRW metric.
The de-Sitter metric is a special form of the non-static Friedmann metric, and appears to be genuinely non-static since it describes the initial exponential expansion of the Big Bang universe.
It means that you defined a non-static function without preceding it by a prototype.
On the other hand, non-static fleld equations were invoked for the first time by Alexander Friedmann in 1921.
The most familiar spherically symmetric static metric is the vacuum Schwarzschild metric: On the other hand, metrics associated with gravitational collapse or evolving cosmology naturally correspond to non-stationary or non-static ones though, of course, the respective final states, by definition, should correspond to static metrics.
Many books and articles do mention that the de Sitter metric which is supposed to be non-static (in the comoving frame) appears to be static in the Schwarzschild frame.
