## Lecture 9

### Topics

- Schwarzschild solution: the geometry for \( r > r_s \)
- Gravitational redshift
- Freely falling paticles: massive particles
- Radial motion analysis using conservation of energy and angular momentum for massive particles
- Freely falling paticles: massless particles
- Christoffel symbols and curvature tensors
- Numerical solution of the geodesic equations

### Bibliography

- Lecture slides (1st lecture)
- Lecture slides (2nd lecture)

### Practicing

- Problems and their solutions.
- Numerical solution of the geodesic equations: Massive particles (Mathematica notebook, PDF)
- Numerical solution of the geodesic equations: Massless particles (Mathematica notebook, PDF)
- Symbolic computation of the affine connection and curvature tensors (Mathematica notebook, PDF)
- Symbolic computation of the affine connection and curvature tensors usinc xCoba (Mathematica notebook, PDF)

### Videos

Related video lectures by the instructor. There is partial overlap with the course curriculum, use at your own discretion! Check the video lectures page for details...