Ah ok. Nevertheless, as far as I understand, global hyperbolicity in 4D is equivalent to requiring ##\mathbb R \times \Sigma## product topology for spacetime.Pavel Dubov said:I think the point Giulini is making in his lecture is more about the requirements for a well-posed initial value problem rather than a restriction of the Einstein Field Equations (EFE) themselves. While the EFE is indeed a local tensor equation, the global hyperbolicity is a physical 'must' if we want the universe to be predictable (admitting a Cauchy surface).
No, it is not, as I've already said several times in this thread. I even gave you an explicit counterexample.cianfa72 said:as far as I understand, global hyperbolicity in 4D is equivalent to requiring ##\mathbb R \times \Sigma## product topology for spacetime.