1
$\begingroup$

In Numerical Relativity by Thomas W. Baumgarte and Stuart L. Shapiro.

There are bunch of superscript $(4)$ over $T,\Gamma, R$
i.e. $^{(4)}\Gamma^a_{bc}$ _ $^{(4)}R_{abcd}$ _ $^{(4)}R$ ... (see example in page 5).

I thought it was just indicating it's $4$ vectors, where I encountered a sentence in page 8 saying "the superscript $(3)$ (on the left instead of on the right) in the above formula indicates the third time derivative..."

I flipped through the book and this notion continuously poped up, i.e. $^{(2)}ds^2$ ...

  1. what does the superscript on the left mean? i.e. $^{(4)}R$

  2. when the book said third time derivative(or higher), does it just mean $^{(3)}I =\frac{d^{(3)} I}{dt^{3}}$? But why it wasn't indicated in the indice. i.e. page 9 equation 1.50

$\endgroup$
  • $\begingroup$ “On the right instead of on the right”? $\endgroup$ – G. Smith Nov 21 '18 at 7:02
1
$\begingroup$

As @G.Smith says, it refers to 4-dimensionality.
In the first paragraph on page 27, it says "Four-dimensional objects associated with $g_{ab}$ are denoted with a superscript ${}^{(4)}$ in front of the symbol,..."

$\endgroup$
2
$\begingroup$

It most likely indicates the number of dimensions. For example, $^{(4)}R$ indicates a 4-dimensional Ricci scalar.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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