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PeterDonis
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The parenthetical qualifier here is crucial. Without it, "any" just means one single geodesic, not a family of them.cianfa72 said:any (an entire family of)
The parenthetical qualifier here is crucial. Without it, "any" just means one single geodesic, not a family of them.cianfa72 said:any (an entire family of)
"Every timelike geodesic" is way too strong. You need to say "every one of some particular family of timelike geodesics". And to really have it be meaningful, the family of timelike geodesics needs to fill the entire spacetime.cianfa72 said:We said that in an arbitrary spacetime there is no guarantee to find a global coordinate chart in which every timelike geodesic is "at rest" in it.
Of course: FRW spacetime.cianfa72 said:Does exist an example of curved spacetime in which there is a timelike geodesic congruence filling it all ?
Yes.cianfa72 said:In that case however, since the spacetime curvature, the geodesics deviation (i.e. tidal gravity) must be not null.
Yes that's right, I was inaccurate in describing it. As you said the main requirement is that 'that some particular family of timelike geodesics' needs actually to fill the entire spacetime.PeterDonis said:"Every timelike geodesic" is way too strong. You need to say "every one of some particular family of timelike geodesics". And to really have it be meaningful, the family of timelike geodesics needs to fill the entire spacetime.