Re: topological equivalence?


"Tom Roberts" <tjroberts@xxxxxxxxxx> wrote in message
news:dc85rd$2nt@xxxxxxxxxxxxxxxxxxxxxxxxxxx
> ajiko wrote:
>> Start with a curved GR world. [...]
>> Now take that curved space and flatten it out. [...]
>
> There are two major problems with this:
>
> 1. It is only possible for manifolds with topologies consistent
> with a flat metric. In particular, FRW manifolds with positive
> spatial curvature have spatial topology S^3 and this simply is
> not possible.
>
> 2. The GR manifold is spaceTIME, and you are discussing only the
> "space part" -- that's a problem as it can depend on how
> you foliate spacetime into space and time.
>
> There are lots of minor problems, too. For instance, any singularities
> will result in holes punched into your flat manifold -- in the curved
> manifold they make sense, but in a flat manifold they don't. And the
> foliation is subtle but important: for instance, I doubt a manifold with
> two black holes that inspiral and merge can be manipulated this way, not
> for topological reasons, but because the foliation you envision is
> probably not possible.
>
>
>> Compact
>> the space where it is curving so that it becomes flat. Black holes would
>> require a deep reach to pull the space back into the small volume that we
>> imagine it to be in.
>
> But what do you do with the singularity inside? It is topologically
> significant. Some singularities are topologically non-trivial....
>
>
>
>> The new space would then be described with a different kind of space-time
>> metric. There would be a space-time scaling field that maps the original
>> space-time to the manipulated space-time (or vice-versa).
>
> Except for singular points. And ONLY for manifolds for this this is
> topologically possible. For instance, for a spatial manifold with topology
> S^3 this is NOT possible, because there can be no such "scaling field"
> (the problem is the requirement that it be a field).
>
>
> Tom Roberts tjroberts@xxxxxxxxxx

The point of the post was really more that the vector metric is possible.
The question is: What fundamental accepted principle is being tossed out by
GR? Is GR necessary for any observations that this metric doesn't cover?
For example, with this vector metric, black hole analysis is possible.
There is a kind of spread-out singularity at the event horizon. Also, for
an expanding universe, there is an additional speedup of the expansion
without any need for dark matter.

The metric in this post is a straight derivation from the listed principles!

These principles:

0) Principle of relativity is valid.
1) Speed of light is measured with the same value in upper and lower
reference frames (locally Lorentzian).
2) Captured energy gravitates (hot object is slightly heavier, compressed
spring is slightly heavier).
3) Energy is conserved.
4) Gravitation potential of V=-GM/R (his analysis is actually independent of
the details of the potential function)
5) Energy of light is proportional to its frequency.
6) A perpetual motion machine of the first kind is impossible.

Imply this metric:

ScaleT = 1 - (-V)
ScaleXYZ = 1 / (1 - (-V))

Where V is the unitless version of the standard Newton gravity potential.
and -V is positive.

Ned Phipps


.

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