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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 \\...
smitke6's user avatar
  • 131
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 ...
Tim Campion's user avatar
  • 61.9k
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 ...
Willie Wong's user avatar
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 ...
Pedro Lauridsen Ribeiro's user avatar

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