My question is about the extent to which "now" is defined in GR.
In Minkowski spacetime, it's possible to define a "now" for an inertial observer by finding a spacelike 3-plane such that, in the observer's frame, all 4-vectors in the 3-plane have zero time component (or something like that - apologies, my geometry is a bit rusty - anyway, a 3-plane in which all vectors are orthogonal to the tangent vector of the observer's world line). This plane can be defined globally, so that my "now" is a slice through the whole of Minkowski space.
My question is whether it's possible to define such a thing in general relativity. So, for instance, can I meaningfully speak about what the Andromeda Galaxy is doing "right now"? Or is the "present moment" something that can only be locally defined? I remember seeing something in a Roger Penrose book about this, but I can't find the reference (if anyone knows it, please let me know!)