Recent content by Nabigh R

Stress-Energy tensor deals with the energy content of space. It's the Einstein tensor ##G_{\mu \nu} \equiv R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R## that you want to write in terms of the metric tensor. Anyway, as Ben said it's going to be extremely messy. See...

Thanks Bill, Wikipedia too says a similar thing, but what exactly is an affine parameter?

I am trying to derive the geodesic equation by extremising the integral $$ \ell = \int d\tau $$ Now after applying Euler-Lagrange equation, I finally get the following: $$ \ddot{x}^\tau + \Gamma^\tau_{\mu \nu} \dot{x}^\mu \dot{x}^\nu = \frac{1}{2} \dot{x}^\tau \frac{d}{ds} \ln \left|...

Yeah David, I think even MAXIMA defines Ricci tensor in terms of contraction over 1st and 4th indices since it defines the Riemann tensor as in Weinberg (1972), but the components of Ricci tensor have opposite signs to the ones given by Weinberg.

As an aside to the original question: the Christoffel symbols doesn't depend on the sign of metric, right? What about other tensors found using them?

Thanks a lot robphy. That really helps.

Thanks ultrafast... I have already seen those and in fact it's because of the latter link only I posted this question... it's really hard to keep track of changes to the field equations with different conventions... I mean in one, the constant on right hand side is negative, other positive, even...

Hi guys... I was wondering if anyone have a sort of a summary of sign conventions in general relativity books. By convention I mean the definition of Riemann tensor, Ricci tensor and signs of stress-energy tensor and signs of einstein field equations for a given sign of metric tensor... I heard...

Thanks a lot Greg. That's just what I was looking for. Just saw blockwise inversion theorem of matrices on Wikipedia. Since it didn't occur me to change the order of coordinates, I didn't make the connection. Thanks again :approve:

Thanks Mentz :-D I know I can get ##g^{\mu \nu}## by inverting the matrix representation of ##g_{\mu \nu}##. But what I want to know is reasoning Schutz used to simplify the problem of finding the inverse of a ##4 \times 4## matrix to that of finding the inverse of a ##2 \times 2## matrix :-)...

How do you find the inverse of metric tensor when there are off-diagonals? More specifivally, given the (Kerr) metric, $$ d \tau^2 = g_{tt} dt^2 + 2g_{t \phi} dt d\phi +g_{rr} dr^2 + g_{\theta \theta} d \theta^2 + g_{\phi \phi} d \phi^2 + $$ we have the metric tensor; $$ g_{\mu \nu} =...