when do you call a spacetime dynamical....when metric is time dependent or it depends on space ??...
Ok...then AdS geometry has spatial dependence then why it is written that fixed boundary theory has a correspondence to bulk gravity theory which is dynamical..(in the context of AdS/CFT)...
One of the reasons the concept of spacetime eventually became a natural concept to me is due to some conclusions one can make regarding any direct observation of length and time.
Length only exists (observationally) in conjunction with time, that may not be intuitive but what differentiates lengths like a meter from a kilometer is time. We tend to think of those lengths as static but if time is 0 both lengths are infinite. Time > 0 is required to observe and differentiate length; however the same holds true for direct observations of time, such observations include a length > 0 too. Please remember I am referring to direct observations above.
Traditionally time is associated with dynamical systems whereas space is not. I’d only be guessing if that holds true in the context of AdS/CTF theory. Perhaps what I brought up above might give you a little better insight into it.
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