- #1

Buzz Bloom

Gold Member

- 2,118

- 363

## Summary:

- I understand that K(infinity) = zero, and K(Schwarzchild radius) = infinity, but what is K(r) between these limits?

## Main Question or Discussion Point

I understand that

ADDED

In

in the section

I am hoping that some reader can confirm that my guesses are correct or incorrect, and if incorrect, what the curvature might be.

I am also wondering if this thread might be better placed in the Special and General Relativity forum. I also apologize for mispelling "spatial" in the title.

K(∞) = 0,

andK(r

where_{s}) = ∞r

_{s}= 2GM/c^{2}.

What is an equation for K(r) whenr

_{s}< r < ∞?

I have tried the best I can to search the Internet to find the answer, but I came up empty. I would very much appreciate the answer, or a reference that discusses the desired answer. I have seen some tensor equations, but my math skills cannot deal with those.ADDED

In

in the section

Flamm's Paraboloid

the following equation is derived:w(r) = 2r

The coordinate system is described as_{s}√((r/r_{s})-1).The Euclidean metric in the cylindrical coordinates (r, φ, w) is written:

ds

I am guessing (and may certainly be mistaken) that w(r) is related to the spatial curvature. In particular, I am guessing that w(r) is the radius of curvature, and the curvature is^{2}= dw^{2}+ dr^{2}+ r^{2}dφ^{2}.k(r) = 1/w(r).

I am hoping that some reader can confirm that my guesses are correct or incorrect, and if incorrect, what the curvature might be.

I am also wondering if this thread might be better placed in the Special and General Relativity forum. I also apologize for mispelling "spatial" in the title.

Last edited: