What's being curved, when mass bends the spacetime continuum?

[Kraflyn]

Hi.

Oh, we have very good definition for that. All of 64 Riemann curvature tensor components vanish simultaneously? Then space is flat at that point. Some of Riemann curvature tensor components are different than zero? Sorry, not flat. Einstein was poetic that day. Too much gulash, I guess. Heh, gulash is cooked with - wine!

Cheers.

 

[Muphrid]

But the geometry of spacetime is also described by a field. Newtons gravitation is a vector field. Einsteins gravitation is a tensor field:
http://en.wikipedia.org/wiki/Field_(physics )

Which tensor field in GR would you call the gravitational field?

 

[Kraflyn]

Hi.

Heh, it depends on nomenclature... For instance, in metric \delta s^2 = \left(1+2V(r)\right)\delta t^2-\frac{\delta r^2}{1+2V(r)}-r^2 \delta \Omega^2 metric tensor components are fields describing gravity... Strictly speaking, there is no exterior field for gravity. This is the very condition for gravity: E_{\mu \nu}=0. Nothing on the right-hand side. On the other hand... What is 1+2V(r) then?... It's some field, right? So... I'm becoming a bit bored of this now.

Cheers.

 

[StephenofCaly]

My simplistic understanding is that to get from Hither to Yon, you have to go a certain way. The rule for light is it has to get there the fastest way, not the straightest path. Since almost always they are the same, it's confusing when they diverge.

Another is like saying - how come the way to Mecca is off to the northeast for local Muslim folks? Mecca's actually at a slightly lower latitude to where I live, but not much. Ought to be SOUTHeast, by my guess. What is the thing that causes the Qibla (the way to Mecca) to curve? That's a fallacious question.