- #1
Philip Land
- 56
- 3
The RW metric reads
$$ds^2 = -dt^2 + a^2(t) \Big( \frac{dr^2}{1-kr^2} + r^2 d\theta^2 + r^2 sin(\theta)^2 d\phi^2 \Big)$$
The value of k determines the model is flat/open/closed.
But say if we have a model on a completely different form, with no explicit k-dependence. How would I determine if it's closed(open/flat?
Take a very simple example: $$ ds^2 = -dt^2 a(t)^2 \Big( dx^2 + dy^2 + dz^2 \Big)$$
How would you see what model this lin-element would correspond to?
$$ds^2 = -dt^2 + a^2(t) \Big( \frac{dr^2}{1-kr^2} + r^2 d\theta^2 + r^2 sin(\theta)^2 d\phi^2 \Big)$$
The value of k determines the model is flat/open/closed.
But say if we have a model on a completely different form, with no explicit k-dependence. How would I determine if it's closed(open/flat?
Take a very simple example: $$ ds^2 = -dt^2 a(t)^2 \Big( dx^2 + dy^2 + dz^2 \Big)$$
How would you see what model this lin-element would correspond to?