Cosmo 101 The Schwarzschild metric

Ok so here is where things start to get weird. Last night I introduced the Schwarzschild metric, but now allow me to explain why it’s necessary. We are use to a world that is basically flat. If you have a circle and you measure the circumference then divide by 2 time pi you get the radius. If you measure from the center of the circle to the edge of it you get the same number for the radius. Duh! But now I shall show you an example in which this is not true. Ok so now take a look at the picture that I’ve included. The black thing in the center is a really heavy black hole. Now let’s say there is an alien race that flourishes around black holes. So what they do is big these big platforms all around the black hole. The purple and red dashed lines are 2 different platforms that our alien race has built. Not what the scientists of our alien race (they need a name) want to measure the distance from their platforms to the center of the black hole. So what would we suggest they do? We would suggest they measure the circumference of the platform and divide by 2 times pi (in light blue), and then do the same with the other platform (in dark blue). Our alien friends are a bit skeptical so we suggest that as a check they subtract these 2 radii and that should be the distance between the platforms (in orange). They do as we suggest and find something amazingly peculiar. Their outer radius subtracted from their inner radius does not equal the distance between the platforms! The human scientists are astonished, embarrassed and confused, but the alien scientists are quick to explain. Because of the heavy influence of gravity near the black hole our normal geometry (which we call Euclidian geometry) simply doesn’t work. It just doesn’t work. In this instance, our alien friends explain, we have to use the Schwarzschild metric.