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Consider spacetimes which are asymptotically flat at null infinity.

How to explicitly show that there exists a hyper-surface orthogonal killing vector field $k^{a}$ that is time-like everywhere in Minkowski spacetime? That then means the Minkowski space time is strictly static.

But all the hyper-surface orthogonal killing vector fields must be space-like in regions II and III of the Kruskal spacetime? This then means Kruskal spacetime is not strictly static.

Is the Kruskal space-time strictly stationary? That is, there exists a killing vector field that is everywhere time-like. (So, the condition hyper-surface orthogonal is released.)

Reference: Prof. Harvey Reall's Part III Black Holes pp. 91.

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  • $\begingroup$ I think the answer for the first is obviously $\partial / \partial t$. $\endgroup$
    – John
    Commented Dec 21, 2023 at 21:33

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