QuoteI read Einstein's 1939 paper along with Oppenheimer and Snyder’s 1939 frozen star paper on continued gravitational contraction, and thought something's missing here, because falling bodies don't slow down
This is supposed to be a relativistic effect, because when massive body collapses, then the time runs increasingly more slowly for it (due to gravitational dilatation of time within curved space-time) - so that at certain level the further condensation would require more time, than the age of observable Universe. One could consider it as a canonical reasoning, why black holes singularities cannot exist or - if they turn out to be still existing - they must be older than the Universe (or most probably that Universe is older than particle horizon of it). It's known that despite the fatherhood of black holes is attributed to Einstein in mainstream media, he never fully accepted this concept in similar way, like many other relativistic theorems (gravitational waves, Big Bang universe or even space-time concept itself), which are routinely connected with him.