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a) If a brane action in a bulk is defined, in that case, that a brane is modelwise moving through a bulk, how is this ratio defined? Is this a regular "velocity" in that meaning, that space is being passed in a period of time?

b) If a 4D-Einstein-Spacetime is chosen, where space itself is a slice cut through spacetime, how can the ratio, with which the space is moving through time, be defined? I suppose a "space per time" fails due to it is more a "time per X", but what is X?

I am trying to put a different light on the attributes how "space" and "time" are defined. As far as i do understand GRT and FRW-Models, "space" is just a static cut through spacetime in form of a slice. Perhaps there occur some interesting effects, if space is modelwise treated more as a dynamic part of the spacetime. Therefore it makes sense to me to ask how a spacelike hypersurface (being "space") really moving through time could be described. To do this, one needs to define a ratio, how this "moving" can be expresses, comparable to a velocity inside the space of our perception, setting ds/dt and gaining v. In some papers i came across statements like "branes moving through the bulk" and i wonder how this "moving" is defined, because one could ask "how fast ist the brane moving?".

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