2
$\begingroup$

If I got a diagonal stress energy tensor $T_{\alpha \alpha} = x_{\alpha}$ for some coefficients $x_{\alpha}$, could anyone tell me how can I extract the four components of the stress energy tensor? Also, is there a way to derive the metric for such a case?

$\endgroup$
1
  • 2
    $\begingroup$ how can I extract the four components of the stress energy tensor What do you mean by "extract?" You already have them, don't you? $\endgroup$
    – user4552
    Oct 8, 2013 at 15:35

1 Answer 1

2
$\begingroup$

Also, is there a way to derive the metric for such a case.

No, the metric isn't uniquely defined by the sources. For example, if the stress-energy tensor is zero everywhere, your metric could be Minkowski, or it could be something with gravitational waves in it. For example, here is a vacuum solution, expressed in coordinates where it's diagonal, that isn't Minkowski:

$$ds^2 = d t^2 - p(z-t)^2 d x^2 - q(z-t)^2 d y^2 - d z^2 $$

Here $p$ and $q$ are any functions that satisfy the differential equation $\ddot{q}/q+\ddot{p}/p=0$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.