## New answers tagged lorentzian-geometry

3
votes

### The stabilizer of a point in the connected Lorentz group

One may prove by direct computation that in order to stabilize $p$, your matrix $f$ must be a block matrix of the form:
$$ f = \begin{bmatrix}
1 & 0 & \vec{v}^T \\
0 & 1 & -\vec{v}^T \\...

5
votes

### Can the Causal Structure recover the manifold topology for non-chronological spacetimes?

Regarding the title question: No, the topology cannot be recovered from the chronology relation for non-chronological spacetimes. For example, there are plenty of distinct Lorentzian manifolds for ...

7
votes

Accepted

### Topology and local isometry, spinning cosmic string

I think in your question, as currently formulated, the whole rotating cosmic string is a red herring.
If I interpret your notation correctly, $a$ and $\kappa$ are constants. And hence locally you can ...

0
votes

### Distinguishable under manifold topology but indistinguishable under the Alexandrov topology

What you seem (to me) to be asking is under which conditions on a Lorentzian manifold its Alexandrov topology not even $T_0$. If that is the case, then it is easy to see that if $(M,g)$ is not ...

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