Date: Apr 25, 2013 7:34 AM
Author: dan.ms.chaos@gmail.com
Subject: Re: closed universe, flat space?

> Let?s look at spacetime. According to GR, it is the curvature of

> spacetime that causes gravity. So, spacetime is curved around a

> gravitating mass. In free space, the Einstein tensor vanishes which

> means the Ricci tensor also vanishes which mean the Riemann tensor

> also vanishes. So, you have vanished Riemann tensor in curved

> spacetime. That means the curvature tensors really do not address the

> curvature thing. The field equations are merely differential

> equations that allow you solve the local geometry and nothing more.

> <shrug>

http://en.wikipedia.org/wiki/Ricci-flat_manifold

The Ricci tensor vanishing does not imply the Riemann tensor does .

Also ,don't confuse space with space-time . Space is only a 'slice' of

space-time . In itself it can be flat, while still being in a curved

space-time . The metric of space is three-dimensional , and embedded

in the four dimensional metric of space-time. Even factoring out the

gravitational effects (which predominantly affect the time-time

component of the metric tensor, not it's space components ) ,we still

have to consider the expansion of the universe .

http://en.wikipedia.org/wiki/Metric_expansion_of_space

Space can be predominantly flat (provided it's free from strong

gravitational effects) , while still being embedded in a curved space-

time .

> Write down the metric for n-sphere please. <shrug>

If the earth were perfectly round , you would return to your point of

origin when going around it . Generalize . Or better yet, use Google

to figure out the metric .

> At least, you admit your own version of cosmology is purely

> speculation. The so-called experts believe in their speculated

> ?reality? more whole heartedly.

First, don't underestimate the value of rational speculation .I

speculate that the sun will rise tomorrow .

All science has origin in rational speculation.

Second, the most commonly accepted model of the universe is flat (in

space) and infinite.Observations confirm

the universe 'flat with only a 0.4% margin of error' .

http://en.wikipedia.org/wiki/Shape_of_the_Universe#cite_note-2

><shrug>

I find it much easier to read your post with this image in mind

http://www.bittersweetcandybowl.com/candybooru/_images/1b9e551d747b18f28b1ad49bd2835f22/3906%20-%20Jasmine%20Marshmallow_%28Artist%29%20excellent%20pony.png

If you post had a point to make, I don't see it. <shrug>