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.
