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3. pp-wave

pp-wave

pp-wave spacetimes are a class of spacetimes possessing some manner of plane waves, such as pure gravitational waves, electromagnetic waves, scalar field waves, etc. They are parametrized by a function $H(u,x,y)$.

1. History

2. Topology

pp-wave spacetimes are rather generic but usually they are done in the topology $\mathbb{R}^4$.

3. Metrics and coordinates

Brinkmann coordinates

$$H(u,x,y) du^2 + 2dudv + dx^2 + dy^2 $$

4. Tensor quantities

5. Symmetries

6. Stress-energy tensor

7. Curves

8. Equations

9. Causal structure

10. Asymptotic structure

11. Energy conditions

12. Limits and related spacetimes

13. Misc.

Bibliography