Lecture 10
Topics
- Schwarzschild solution: the geometry for \( r < r_s \)
- The horizon at \( r = 2M \)
- Radial null lines and light cone structure
- Radial fall of an observer in the black hole: relative accelerations
- Stationary observer
- Eddington-Finkelstein coordinates
- Kruskal-Szekeres coordinates
- Extended Kruskal diagram
- Penrose diagram of the Schwarzschild spacetime
Bibliography
- Lecture slides (1st lecture)
- Lecture slides (2nd lecture)
Practicing
- Problem set 1 and their solutions.
- Problem set 2.
- Radial null geodesics + light cone structure: Schwarzschild coordinates (Mathematica notebook, PDF)
- Radial null geodesics + light cone structure: Eddington-Finkelstein coordinates (Mathematica notebook, PDF)
- Eddington-Finkelstein coordinates: affine connection and curvature tensors (Mathematica notebook 1, Mathematica notebook 2, PDF 1, PDF 2)
- Kruskal-Szekeres coordinates: affine connection and curvature tensors (Mathematica notebook, PDF)
