Good question! It's the stress-energy that generates curvature, and matter is just short hand for stress-energy or energy-momentum. Matter remaining at e.g. th

Good question! It's the stress-energy that generates curvature, and matter is just short hand for stress-energy or energy-momentum. Matter remaining at e.g. the origin of spatial coordinates (x=0, y=0, z=0, t=var) is still moving through spacetime [1]. T^{tt} encodes the flux of energy-momentum through the point along the time direction, and identifies as energy-density. Also, you get to think about if and how "remaining [at fixed] spatial coordinates" is actually meaningful in relativity. "Don't rely on slogans" is a good General Relativity slogan. - -- [1] assuming anything is moving at all; to get to that we will want to slice the block universe spacetime into space and time (and did that implicitly above), and not everyone will like how you did the slicing. Like if you wanted to make onion rings but someone has sliced up your onions with all the cuts parallel to this initial one https://images.fineartamerica.com/images-medium-large/onion-slice-kyle-matheney.jpg https://images.fineartamerica.com/images-medium-large/onion-... instead of this way https://www.pngkit.com/png/detail/12-121112_sliced-onion-png-download-image-red-onion-slices.png https://www.pngkit.com/png/detail/12-121112_sliced-onion-png... You'll also want to plant values on one spacetime slice, and let dynamics evolve them slice-to-slice. See: https://en.wikipedia.org/wiki/Initial_value_formulation_(general_relativity) https://en.wikipedia.org/wiki/Initial_value_formulation_(gen... [2] > additional curvature Can of worms. :)