Tagged Questions
7
votes
1answer
124 views
Uniqueness of Riemann curvature tensor
Normally in differential geometry, we assume that the only way to produce a tensorial quantity by differentiation is to (1) start with a tensor, and then (2) apply a covariant derivative (not a plain ...
2
votes
1answer
45 views
General expression of the redshift: explanation?
In some papers, authors put the following formula for the cosmological redshift $z$ :
$1+z=\frac{\left(g_{\mu\nu}k^{\mu}u^{\nu}\right)_{S}}{\left(g_{\mu\nu}k^{\mu}u^{\nu}\right)_{O}}$
where :
$S$ ...
1
vote
1answer
51 views
What is the Lorentz tensor with a superscript and subscript index?
I have been reading about symmetries of systems' actions, e.g. the Polyakov action, and I have encountered Lorentz transformations of the form: $\Lambda^{\mu}_{\nu} X^{\nu}$. I am moderately familiar ...
3
votes
1answer
100 views
When a variation of a tensor is not a tensor?
In a comment about variation of metric tensor it was shown that
$$\delta g_{\mu\nu}=-g_{\mu\rho}g_{\nu\,\sigma}\delta g^{\rho\,\sigma}$$
which is contrary to the usual rule of lowering indeces of a ...
2
votes
1answer
44 views
Non-diagonal elements when switching metric signature?
Considering a metric tensor with the signature $(-,+,+,+)$:
$g_{\mu\nu}=
\begin{pmatrix}
-c^2 & g_{01} & g_{02} & g_{03}\\
g_{10} & a^2 & g_{12} & g_{13}\\
g_{20} & g_{21} ...
1
vote
2answers
113 views
What should I call an n>4 dimensional Minkowski metric?
I am manipulating an $nxn$ metric where $n$ is often $> 4$, depending on the model. The $00$ component is always tau*constant, as in the Minkowski metric, but the signs on all components might be ...
