I have a variable "a" which only is a function of time, ie all space derivatives are zero.

I have been trying various ways of dealing with expressions like \begin{equation}{}\partial^{r}{{a}^{-2}} h_{r}\end{equation}

I have used the substitute command to convert it to: \begin{equation}{}\eta^{r}{}_{0} \partial^{0}{{a}^{-2}} h_{r}\end{equation}

Problem is that eliminate metric doesn't seem to push through to give an h_0 term

I am using fixed indices.

Even worse when instead of $h*r$, the second term is a partial derivative like
\begin{equation}{}\partial^{r}{{a}^{-2}} \partial\*{r}{h}\end{equation}

Then I get \begin{equation}{}\eta^{r}{}_{0} \partial^{0}{{a}^{-2}} \partial_{r}{h}\end{equation}

And I cannot get the r index pushed through via eliminate metric.

I don't want to use kronecker deltas because I will loose the sign structure of metric.

Also I have many versions of the above expression, so I have been creating long substitution rules (seems like I need all the combinations of fixed indices, plus different tensor and derivative forms).

I don't really want to use the split index function to separate out space and time indices at this point in my calculation since the number of terms will explode, and I already have very many. It is a perturbation problem to third order.

Also many times canonicalize seems to crash the program with all of these metric terms.

Final question -- since fixed indices seems to make it tough to simply things, when is it safe to switch back to free indices. My raising and lowering metric is Minkowski.

Can I do part of a calculation with fixed indices then switch to free later on with another Indices declaration. Same with post_process -- can I start with one (without canonicalize) and then use another later.

Thanks for your thoughts.

Any ideas?

So, is there a better way to do this