0
$\begingroup$

The Wikipedia article on metric signatures says that the signature of a metric can be written $(v,p,r)$, where $v$ is the number of positive eigenvalues, $p$ is the number of negative eigenvalues, and $r$ is the number of zero eigenvalues.

Explanations of the metric signature usually give short shrift to 'r', as if it is an unimportant mathematical artifact....

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ I have edited your question to include the relevant context. In the future, please include this information yourself. As a general rule of thumb, you should define all of the symbols you use, either explicitly via text or implicitly by their appearance in a universally-recognized equation (e.g. $F=ma$). $\endgroup$
    – J. Murray
    Commented May 27 at 12:34

2 Answers 2

Reset to default
3
$\begingroup$

In general relativity, the metric is assumed to be Lorentzian, which means that it has signature $(1,n-1,0)$ or $(n-1,1,0)$ depending on convention. Because the metric does not have any zero eigenvalues, we generally don't refer to $r$ at all, and simply refer to the metric signature as $(+---)$ (mostly minus) or $(-+++)$ (mostly plus).

Improve this answer
$\endgroup$
1
$\begingroup$

Just to add something, in some contexts, e.g., asymptotic symmetries, the relevant quantity is the pullback metric $q_{ab}$ of the conformally rescaled metric to $\mathcal{I}^+$, which has signature $(0,+,+)$.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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