http://www.rafimoor.com/english/GRE2.htm#The_Geometric_Meaning_of_Curvature_Tensors
I think, if true, this should be the first example mentioned for anyone beginner who strives to understand GR.
Hello,
I've just read and I think I have understood the following result :
If we were to geodesically transport all points of a small 2D surface, so small that it would be flat for all purposes, in a direction vertically above it, and if this surface belongs in an arbitrary 3D manifold, then in...
Thank you. I did not mean that physicists use this terminology but rather what the popularizing physics book say.
So, I think we have agreed that space-time as a whole has no beginning nor ending and therefore was 'never' created, -never- in quotes, because time does not exist independently of...
I think that's why I am talking about a manifold in the first place because coordinates are irrelevant. How then do you say that spacetime had a beginning since all the g's in the metric vanish somewhere, when all there is, is the manifold itself oblivious of anything around or beyond it?
Look...
I must admit that I've made a mistake. Not only the space coordinates disappear somewhere on the manifold but the time coordinate as well. It's hard to visualize this but as an example I have the 2D hyperbolic torus x2 + y2=-r2 , z2 + w2=-r2 embedded in a 4D Euclidean space with signature (1,-1...
Ok, I have a better wording for this now. There is a manifold in FLRW solutions where at some point on its surface has all space and time coordinates vanishing and you take this as the moment of creation or big bang, right? But this manifold is all that there is, and because all the g's are...
Orodruin, I think you haven't quite captured what I said.
Isaac0427, on the contrary has exactly understood what I am saying, although his answer is the exact opposite of what I am saying. I am saying the space is not static, any solution of the FLRW is ( sorry for my wording here! ) Any...
Hello,
Cosmology for the layman says that there was a time t=0 when the universe was created out of infinitesimal length distance and before that nothing existed not even time.
OK, but this rests on the assumption that there is always a manifold from which we cut off our space slices in the...
Hello. I am not familiar with differential geometry and curvature tensors, yet I am having a great deal of questions to ask.
First when we lay a set of coordinates for an n-dimensional plane, let's say 2 coordinates for a surface embedded in a 4D space the vectors we begin with to describe our...