## Lecture 7

### Topics

- The Stress-Energy Tensor
- Conservation laws in Special Relativity
- Stress Energy tensor for the perfect fluid, and the electromagnetic field
- Isometries and conservation laws in curved spacetime
- Killing vector fields (KVF)
- Conserved \(\xi_\mu u^\mu \) along geodesics
- Conservation of \( J^\mu = \xi_\nu T^{\nu\mu} \)
- Conservation of energy/momentum when the metric admits timelike/spacelike KVF
- KVF of the Schwarzschild metric
- Conservation of energy and angular momentum along geodesics of the Schwarzschild metric

### Bibliography

### Practicing

### 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...