Galaxies without dark matter halos?

In article ,
Dag Oestvang wrote:
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.

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.


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.

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?

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.

-Ted

--
[E-mail me at , as opposed to .]

wrote:

In article ,
Dag Oestvang 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.

wrote:

In article ,
Dag Oestvang 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.