# Is gravity time-like?

Disclaimer: I'm just a physics enthusiast, so pardon my lack of full mathematical understanding.

Basically I've read quite a lot about general relativity, and I have some intuitive knowledge at least about what do we mean for spacetime to be curved, as opposed to space being curved.

I've recently come up to a video that explained that experiments to test the "shape" of space show that is virtually flat. I don't recall which video it was but the same principle is explained in the Wikipedia page for "Shape of the universe":

The actual value for critical density value is measured as $ρ_\text{critical} = 9.47×10^{−27}\rm\, kg\,m^{−3}.$ From these values, it seems that within experimental error, the universe seems to be flat.

• Does this mean that space-time curvatures are only time-like?
• Is this the cause of time dilation in regions around massive objects?
• If the curvature of space time is what defines gravity, is it just time-like?
• "Time-like" has a specific meaning in relativity, that doesn't seem to apply to space-time curvature. It's like asking if a sound is blue. Can you clarify what "time-like" means in your question? – knzhou Sep 29 '16 at 15:54
• Oh, sure, I mean that if the curvature exists only in the time dimension – Alvaro Sep 29 '16 at 16:23

2. That means if those observers were to "freeze time" and drag an arrow around a loop through space at any one moment, the arrow would not rotate. If they were to allow the arrow to move through time, it would rotate. Put differently, triangles drawn by those observers have interior angles adding up to 180$^\circ$, but those triangles will warp over time (specifically in the case of the flat FLRW Universe, they will expand).