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sourena
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I need to calculate δR: R is Ricci scalar
nicksauce said:This should be shown in most GR textbooks...
JustinLevy said:
Okay, so we at least have a starting point we can agree on:sourena said:No, I don't have problem with these equations, but I have problem to calculate this equation from them:
δR=Rab δgab+gab δgab -∇a ∇b δgab
JustinLevy said:Hmm...
maybe there isn't an error. Does
[itex]\delta g_{ab} = - \delta g^{ab}[/itex] ?
I'm too tired to check right now.
So does that mean tensors cannot be used for the sort of questions posed in those threads or that they would be overkill?arkajad said:There is another simple question: "What is the purpose of life?" For an engineer his purpose can be, for instance, to learn about elasticity and to apply his knowledge. And when you start learning elasticity stuff - you will soon find that you can't go too far without tensors. So it all depends on your purpose.
The Ricci scalar, denoted as R, is a mathematical quantity used in the field of differential geometry to measure the curvature of a space. It is defined as the contraction of the Ricci tensor, which is a mathematical object representing the local curvature of a space.
Calculating δR allows us to determine the change in the Ricci scalar. This can be useful in various fields such as general relativity, where the Ricci scalar is a crucial component in the Einstein field equations that describe the relationship between matter and gravity.
The formula for calculating δR is δR = gμνδRμν, where gμν is the metric tensor and δRμν is the change in the Ricci tensor. The metric tensor can be obtained from the given space or can be calculated using the coordinates of the space. The change in the Ricci tensor can be determined by taking the derivative of the Ricci tensor with respect to the coordinates of the space.
As mentioned earlier, calculating δR is essential in general relativity. It is also used in cosmology to study the expansion of the universe and in quantum field theory to understand the behavior of particles in curved spaces. Additionally, it has applications in other fields such as fluid mechanics and computer graphics.
One limitation of calculating δR is that it only gives information about the local curvature of a space. To fully understand the curvature of a space, other mathematical quantities such as the Riemann tensor and the Weyl tensor should also be considered. Additionally, the calculations can become quite complex for spaces with high dimensions.