Looking for Einstein Field Equations, in certain places put that they are 10 and in other places put that they are 16. Which is the correct number?
the page cited is from the East Tennessee State UniversityOriginally posted by Zefram
16. Look at http://www.etsu.edu/physics/plntrm/relat/general.htm if you're not sure what's going in that one). About 3/4 of the way down they get to the field equations.
Sure?I have seen that the formula isNo. It is 10. Field eqn is
Einstein Tensor = Energy-Momentum tensor
I trust in your word, but believe me that there are certain pages where it appears like a contravariant tensor:I've already answer to your first question. Einstein tensor is usually defined as a second rank covariant tensor.
You can always convert from covariant-->contravariant by using the metric tensor.Originally posted by meteor
I trust in your word, but believe me that there are certain pages where it appears like a contravariant tensor:
Einstein equation is 10 coupled non-linear second order partial diffrential equation of metric components. So, for given boundary condition and matter distribution you are solving for metric. Of course there are subtleties. To being able to define energy-momentum tensor of matter we need information on background metric. So, usually you fix backround metric and matter distribution, then perturbatively calculate it's solution. Of course there are few examples of exact solutions, but they are usually rare.Originally posted by meteor
In the EFE, in the metric tensor, you have to put the tensor of the metric that you are using? For example if you are using the Minkowski metric you have to put the Minkowski metric tensor, or if you are using the euclidean metric, you have to put the euclidean metric tensor?
another question: how to multiply a tensor with an scalar? Exists any web that explain this?