Comment by layer8
This detail caught my eye:
> [in their 1975 paper] Ashtekar and Magnon also assume that spacetime is globally hyperbolic
Isn’t the modern assumption that spacetime is globally flat?
This detail caught my eye:
> [in their 1975 paper] Ashtekar and Magnon also assume that spacetime is globally hyperbolic
Isn’t the modern assumption that spacetime is globally flat?
I'm just learning this stuff so the details are hazy, bu my understanding is that there's a difference between spacetime curvature and spatial curvature. You can have a hyperbolic spacetime while at the same time having a flat three-dimensional spatial section of it.
It's not an assumption that space is flat. GR doesn't specify the global space curvature, so it's possible that it has a globally negative or positive curvature, but so far there's no evidence of any.
The term refers to causal structure: https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold