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2. Spacetime database
3. Deutsch-Politzer

Deutsch-Politzer

The Deutsch-Politzer spacetime is a simple example of a spacetime with closed timelike curves stemming from a compactly generated Cauchy horizon, and a compact chronology violating region. It is often used in the study of the effect of closed timelike curves on matter.

1. History

2. Topology

The Deutsch-Politzer spacetime has the topology of a plane with a handle with four points removed, $(\mathbb{R}^2 \# T^2) \setminus {p,q,r,s}$. It is usually constructed by removing two spacelike segments from the Minkowski plane, usually $t = 0$, $|x| < 1$ and $t = 1$, $|x| < 1$, and identifying the upper side of one region with the lower side of the other, and vice-versa.

3. Metrics and coordinates

The Deutsch-Politzer spacetime is everywhere flat, and just has the metric of Minkowski space.

$$ds^2 = -dt^2 + dx^2$$

4. Tensor quantities

Since it is a flat spacetime, the basic tensor quantities are all identical to Minkowski space.

$${\Gamma^\rho}_{\mu\nu} = 0$$ $${R^\rho}_{\mu\nu\sigma} = 0$$ $$R_{\mu\nu} = 0$$ $$R = 0$$

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