- #1

thusidie

## Main Question or Discussion Point

Hi,

I'm getting into general relativity and am learning about tensors and coordinate transformations.

My question is, how do you use the metric tensor in polar coordinates to find the distance between two points? Example I want to try is:

Point A (1,1) or (sq root(2), 45)

Point B (1,0) or (1,90)

I know the distance is 1, but how do I get it using the metric tensor?

ds

dr = sq root(2)-1

dθ = 45-90=-45

I'm not sure what r is in this case.

I'm getting into general relativity and am learning about tensors and coordinate transformations.

My question is, how do you use the metric tensor in polar coordinates to find the distance between two points? Example I want to try is:

Point A (1,1) or (sq root(2), 45)

Point B (1,0) or (1,90)

I know the distance is 1, but how do I get it using the metric tensor?

ds

^{2}= dr^{2}+r^{2}dθ^{2}dr = sq root(2)-1

dθ = 45-90=-45

I'm not sure what r is in this case.