In the Feynman lectures, feynman describes the hot plate model of space curvature and shows that light is bent around the center of the plate, see Fig. 42-6
http://www.feynmanlectures.caltech.e...2.html#Ch42-S1
However, the hot plate corresponds to a region of positive curvature, if I understand things correctly. Outside of a mass, the spacetime curvature should be negative.
I've tried to match the Feynman picture with the Schwarzschild metric. The space part of ds² is (approximately)
[itex]ds^2 = (1+2GM/r) dr^2[/itex]
(where I use a -+++ metric because I'm only interested in space components right now.)
If I understand this formula correctly, it says that the "rulers" in feynman's picture get shorter the further I am away from the central mass, which agrees with the negative curvature interpretation.
From this model alone I would expect light to bend away from a mass - which is of course wrong. Is this due to the time dilation near the mass that affects the geodesics? Or am I making another stupid mistake?
http://www.feynmanlectures.caltech.e...2.html#Ch42-S1
However, the hot plate corresponds to a region of positive curvature, if I understand things correctly. Outside of a mass, the spacetime curvature should be negative.
I've tried to match the Feynman picture with the Schwarzschild metric. The space part of ds² is (approximately)
[itex]ds^2 = (1+2GM/r) dr^2[/itex]
(where I use a -+++ metric because I'm only interested in space components right now.)
If I understand this formula correctly, it says that the "rulers" in feynman's picture get shorter the further I am away from the central mass, which agrees with the negative curvature interpretation.
From this model alone I would expect light to bend away from a mass - which is of course wrong. Is this due to the time dilation near the mass that affects the geodesics? Or am I making another stupid mistake?
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