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Originally Posted by Fortunate
OK. I'll start. Please explain the nature of the terms in the equation G=T. I believe that it equates two symmetric tensors, with G being a metric for a four-dimensional space-time and T being the so-called "stress-energy tensor." Is this understanding correct?
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Close, but no cigar. G=T is an extreme simplification, there are other terms (and indexes on the two tensor terms). G is the Einstein Tensor, T is the stress-energy tensor. The Einstein tensor includes the Ricci curvature tensor (and a few other terms). A metric is basically a solution of the equation. It describes the shape of spacetime. What you have to remember is that G=T is a symbolic form of the equation and cannot be directly used to solve for anything.
Try here for a more in depth explanation.
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Originally Posted by Fortunate
Why are the two sides equal to each other? Thank you.
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Simply? The right side of the equation show how much energy is available, which directly relates to how much curvature is on the left side. Of course, if you know how much curvature is on the left side, you can find out how much energy is on the right. Hope this helped.