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In Schwarzschild geometry, the distance between two circles with different circumferences is larger than the Euclidean...

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Physics

In Schwarzschild geometry, the distance between two circles withdifferent circumferences is larger than the Euclidean result,because the distance between the two circles is given byintegrating dr/ (1 − rs/r) (where rs is a positive constant) alongthe radial path between them.

Invent an embedding of the radial part of the Schwarzschildspatial geometry in one extra Euclidean dimension, that we willcall the z dimension. What is the relationship between dr and dz ofthe one-dimensional “surface” in this two-dimensional Euclideanspace? Sketch the curve in an r > 0 quadrant of the r, zplane.

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4.2 Ratings (717 Votes)
The Schwarzschild geometry describes the spacetime geometry of empty space surrounding any spherical mass Karl Schwarzschild derived this geometry at the close of 1915 within a few weeks of Albert Einstein publishing his fundamental paper on the Theory of General Relativity The history of this discovery and much more is wonderfully recounted in Kip Thornes book Black Holes Time Warps Einsteins Outrageous    See Answer
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