However, I get suspicious when someone argues by analogy. Your "my car remembers a crash, furthermore humans do remember, therefore space could also remember gravity" does not seem reasonable to me.

I am also not sure why my post got downvoted.

Edit: As I think about it, "but Einstein showed that you can bend space without mass" again is an argument by analogy. It doesn't matter what analogies exist. The theory should be tested according to empiric evidence. Pulling your analogies together judt for the sake of abandoning a different theory - where's the point in that?

Did you mean the metric tensor g_{\mu\nu} or the Ricci curvature tensor R_{\mu\nu}?

"Gravitational field" is one of those shifty things in GR that makes one sympathetic to MTW's refusal to identify the term with any particular mathematical object.

You're right though; there are plenty of exact solutions to the Einstein Field Equation which are vacuum solutions -- no matter, just gravity.