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Take a generic Lorentzian spacetime $(M, g)$ where $M$ is a time-oriented 4d manifold and $g$ is the Lorentzian metric that is strongly causal and purely electric.

According to this answer:

Is every strongly causal spacetime purely electric?

The conditions of pure electricity and strong causality at a point $p$ are orthogonal.

I wonder

if global pure electricity imposes any further restrictions on the causal structure of a globally strongly causal spacetime?

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  • $\begingroup$ I find this continuing line of questions rather poorly motivated. The common examples violating any level of the causal hierarchy are all constructed by cutting and gluing pieces of Minkowski space (flat strongly subsumes purely electric). I don't see that you have any reason to suspect a relation between the two conditions. Making the question open ended doesn't really help if one doesn't even have an idea of what kind of connection there should be. $\endgroup$
    – Igor Khavkine
    Commented Jan 20 at 17:08
  • $\begingroup$ @IgorKhavkine I have resons for the speculation but not that it's a robust sign. I would prefer to be given a comment on this post. mathoverflow.net/q/462304/503363 Keep in mind that Wick rotatable spacetimes are all purely electric according to Helleland 2017 arxiv.org/abs/1504.01244 $\endgroup$
    – Bastam Tajik
    Commented Jan 20 at 19:37

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