Topological constrains for the solutions of EFE

[cianfa72]

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).

Ah ok. Nevertheless, as far as I understand, global hyperbolicity in 4D is equivalent to requiring $\mathbb R \times \Sigma$ product topology for spacetime.

 

[PeterDonis]

as far as I understand, global hyperbolicity in 4D is equivalent to requiring $\mathbb R \times \Sigma$ product topology for spacetime.

No, if $\Sigma$ is maximally symmetric, which is how it was defined in this thread, it is not, as I've already said several times in this thread. I even gave you an explicit counterexample.

This thread is now closed.