I was listening to a Lecture and the lecturer said that a sphere cannot have a Lorentzian Metric. Is that accurate? If so, why?

  • 2
    $\begingroup$ Possible duplicate: mathoverflow.net/questions/44861/… $\endgroup$ – lemon Mar 8 '16 at 9:54
  • $\begingroup$ Did he mean a two-dimensional sphere? If so, it's because the light cone could be used to define a non-vanishing vector field, contradicting the Hairy Ball Theorem. $\endgroup$ – PseudoNeo Mar 8 '16 at 9:55
  • $\begingroup$ I'm not sure what he meant, was just a one sentence statement. If the reason is what you're saying, then nothing is implied on $S^3$ $\endgroup$ – Dac0 Mar 8 '16 at 10:08
  • $\begingroup$ S³ does have a Lorentzian metric, given the answers of mathoverflow.net/questions/44861/… $\endgroup$ – PseudoNeo Mar 8 '16 at 10:15
  • $\begingroup$ It seems his statement was simply incorrect $\endgroup$ – Dac0 Mar 8 '16 at 10:21

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