Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

What is physical meaning of $\kappa$ and $R$ in curved space?

$$dl^2 = \frac{dr^2}{1 - \kappa\frac{r^2}{R^2}} + r^2d\theta^2 + r^2\sin^2\theta d\phi^2$$

share|improve this question
    
This is not a direct answer to your question, but relevant and I found it useful: In this and this paper, the author discusses the reasonable coordinate systems for some spacetimes of physical interest. Specifically, check page 21 and 10 respectively. –  NikolajK Dec 17 '12 at 11:00
    
See en.wikipedia.org/wiki/… –  John Rennie Dec 17 '12 at 11:23

1 Answer 1

up vote 3 down vote accepted

That's a metric for a space of constant curvature in 3 dimensions. Typically you would parameterise $\kappa$ as -1, 0, or 1 and $R$ as a non zero real number. So $\kappa$ just tells you if you have positive, negative or no curvature and $R$ tells you the magnitude of the curvature. $R$ can be thought of as a radius of curvature if you choose to embed your 3-space in a higher dimensional space.

For example, if you take $\kappa=1$ and subsitute $$r=R \sin\psi$$ you'll get a 3 sphere metric (in spherical polars) with an $R^2$ overall factor.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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