Lecture 7: the Schwarzschild Black Hole
In lecture 7, we moved to a discussion of the Schwarzschild black hole. We analyzed the red-shift between signals exchanged between observers who stay at different fixed values of $r$. We then analyzed geodesics, and arrived at the surprising conclusion that while an infalling observer crosses the horizon and reaches the singularity in finite time, the observer outside never sees this happen; instead the infaller vanishes after a while because any radiation that he emits get red-shifted below the IR-cutoff of the outside observer. We used this to motivate the Kruskal extension of the Schwarzschild geometry.
The attached Mathematica files verify that the Schwarzschild geometry is a solution of the equations of motion, and also provide a toy-simulation to visualize a light-source falling into the black hole.
Mathematica: Schwarzschild Solution
Mathematica: Animation for a light source falling into the black hole
