It is shown in a previous thread (AdS Space Boundary and Geodesics) that it's possible for null rays to travel to infinity and back in AdS space in finite coordinate time. That is to say, an observer at r=0 would see it go away and come back in a finite time.
How can a light ray travel infinite distance in finite time without travelling superluminally?
Is it to do with the fact that "infinity" is really conformal boundary and so it's some messed up notion of infinite distance?
Or is it to do with there not being a notion of proper time for null rays and "finite coordinate time" not being the correct measurement? I mean locally we still have dx/dt=c by setting ds^2=0 so we can see it isn't breaking the speed of light!
Or is it some other reason to do with the negative curvature of AdS allowing this to happen?