Recent content by jimbobjames

"Most of the time "curvature" means the Riemann curvature tensor or some component thereof." Right pervect, got it. I'm getting there. I appreciate your help along the way.

In one of my earlier posts in this thread I wrote that I thought that only the coefficient of dt^2 in the Schwarzschild metric was relevant when aproximating to Newtonian Gravity as we experience it here on Earth and that "The curvature related to the dr^2 coefficient is relatively...

What part of the theory of general relativity helps us understand why we always see the same side of the moon? Thanks.

From Einstein: "The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant)" So the definition would appear to be: "laws of nature are generally covariant...

Chris, Ill have to disagree with you. I'm convinced that a set of video lectures from a good GR teacher would provide a great service to the community. And it wouldn't have to be 100 hours of lectures - Even if Sean Carroll did another 3 hours in order to provide the next level of detail, I...

"but rather some smaller particles" If you mean some as yet undetected hypothetical particles inside the object, then I think you might need to come up with (or derive) a description of their properties and an explanation as to why they have evaded detection until now. "But what if...

I thought that too Antman - a way to test it would be to heat something on the space shuttle and check if it moves in the direction of the temperature gradient. I had typed the same thing last week and deleted it before posting. The reason I didnt post it was - among other reasons - that you...

"Don't overestimate what you can learn from a forum such as this." OK. I don't have a graduate level course in manifolds and Riemannian geometry, but I learned enough math during my Engineering undergraduate years (almost 20 years ago now) to be able to read those introductory GR books...

Got it - thanks.

OK thanks Chris. Incidently by saying that a spacetime has "time curvature" only, I mean a spacetime whose metric is flat apart from the coefficient of dt^2. The ideas I am trying to relate come from reading Feynman who computes the spacial curvature even at the surface of the sun to be tiny -...

Chris, I've been thinking about what you wrote but I'm still not clear on it. Are you saying that just because (in the weak field approximation) g00 provides the parallel to Newtonian Gravity, that does NOT mean that g11 is insignificant? But that would mean that, even in the weak field...

Thanks Chris - In units where c and G are not 1, we have: ds^2 = -c^2(1-2GM/rc^2) \, dt^2 + \frac{dr^2}{1-2GM/rc^2} And expanding like you suggested we get: -c^2(1-2GM/rc^2) \, dt^2 + (1+2GM/rc^2) \, dr^2 which seems to me to be flat Minkowski space plus a delta. The delta is ds^2...

This is great stuff. Thanks guys. Plenty to chew on here for a while. "And be careful, you did not correctly compute the linearized Schwarzschild line element correctly and your claim that "it only has time curvature" is incorrect; see MTW." I will check that in MTW. I somehow recall reading...

I appreciate it. Ill check where I made a mistake with the christoffel symbols. "Very different from the home cosmos." indeed :smile: I was actually considering only a small local piece of the surface to have that curvature - before you get to the north pole, the space dimension would have...

Thanks again. What I am trying to see are geodesics on 2-d curved surfaces where time is one of those dimensions (and not an extra third dimension). So I am looking at 1 space and 1 time coordinate which I am calling t and h respectively (not 2 space plus 1 time like you have done). If...