Re: Galaxies without dark matter halos?

[EMAIL PROTECTED] wrote:

> In article <[EMAIL PROTECTED]>,
> Dag Oestvang  <[EMAIL PROTECTED]> wrote:
>
> > I will try to clarify: Unless V to a good approximation appears
> > from a cleverly arranged field of 4-velocities in flat space-time
> > (this is exact in the Milne model), there is no natural way to
> > interpret V in this way if the effects on V of curved space-time
> > on parallel transport is not negligible.
>
> That's true.  But in the low-redshift limit, the effects on V of
> curved spacetime on parallel transport *are* negligible.
>

    Not necessarily. While it is true that the effects on V of
    curved space-time  may always be made as small as desired
    by considering small enough regions, these effects cannot
    always be neglected compared to those coming from velocity
    in flat space-time. Recall the example of hovering observers
    in Schwarzschild space-time; that is exactly such a situation.

>
> Proof: Try it and see!  Neglect spacetime curvature and
> parallel-transport V.  In the low-redshift limit, you get the right
> answer.  Therefore, neglecting spacetime curvature didn't
> do any harm.  Spacetime curvature was negligible.
>

     Well, no. For example, if you neglect space-time curvature for
     hovering observers in Schwarzschild space-time, you _don't _
     get the right answer. I believe that if you neglect space-time
     curvature in an Omega=1 FRW model you don't get the right
     answer either. (See the other thread for justification.)

>
> > In other words; insofar as the effects on V coming from the
> > curvature of space-time can be neglected it is perfectly all
> > right to interpret V as coming from a field of 4-velocities in
> > flat space-time. But it is not if the size of V depends crucially
> > on space-time curvature.
>
> I agree.  But again, the last "if" clause is false in the limit
> I'm considering.
>

    Not necessarily.

>
> Do you think that "the size of V depends crucially on space-time
> curvature" in an Omega = 0 FRW Universe?  (I certainly hope not,
> since there is no curvature in this spacetime.)  How about
> in an Omega = 10^(-50) FRW Universe?
>

    No. But I think it does in an Omega=1 FRW model, see the
   other thread.


>
> >   It seems that we mostly agree. This is my position: If the effects
> >   of curved space-time on V are negligible then interpretations of
> >   spectral shifts as Doppler effects in flat space-time are OK;
> >   otherwise not. Do you agree?
>
> Yes.  But again, the "If" clause is false in the low-redshift
> limit of an FRW Universe.
>

    I believe that is not true for FRW models with Omega >=1.