Dynamical Spacetime: Time or Space Dependent?

[kau]

when do you call a spacetime dynamical...when metric is time dependent or it depends on space ??...

 

[bapowell]

Time.

 

[kau]

Time.

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)...

 

[Maxila]

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.

 

[sardar]

A spacetime is considered dynamical when its metric, which describes the curvature of spacetime, is either time-dependent or space-dependent. This means that the geometry of the spacetime is changing over time or varies in different regions of space. This concept is an essential aspect of Einstein's theory of general relativity, which states that the curvature of spacetime is influenced by the distribution of matter and energy.

In other words, when there are changes in the distribution of matter and energy in a particular region of spacetime, the metric will also change accordingly. This can result in changes in the passage of time or the shape of space in that region. Therefore, a dynamical spacetime is one that is constantly evolving and changing due to the presence of matter and energy.

To identify a spacetime as dynamical, we need to observe the effects of its changing metric. This can be done through measurements of the curvature of spacetime, such as gravitational lensing or the bending of light around massive objects. Additionally, the study of the evolution of the universe, including the expansion of space, also provides evidence for a dynamical spacetime.

In summary, a spacetime is considered dynamical when its metric is time-dependent or space-dependent, reflecting the ever-changing nature of our universe. This concept is crucial in understanding the fundamental workings of the universe and is a key aspect of modern physics and cosmology.