## Lecture 4

### Topics

- The metric
- Index raising/lowering
- Eigenvalues of the metric
- Local Frames - Inertial Observers
- The metric and (local) causal structure. Local light cone and "speed of light" limit in GR.
- Examples: wormholes, flat space cosmology, closed timelike curves+Cauchy horizons (Misner spacetimes), faster than c travel, Penrose diagram of the Minkowski spacetime.

### Bibliography

### Practicing

- Problems (solutions, mathemtica notebook+ pdf)
- Penrose diagram of Minkowski spacetime: draw it using Mathematica, compute the metric components in the \( (t',r') \) coordinate system (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...