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Question about the path of a particle in Schwarzschild region of an cosmos
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Oh No
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Joined: 06 Apr 2006
Posts: 82

PostPosted: Mon Jul 10, 2006 3:55 am    Post subject: Question about the path of a particle in Schwarzschild region of an cosmos Reply with quote

As I understand it we can think of the Schwarzschild geometry
surrounding an isolated star as a static perturbation within an
expanding flat or near flat space-time. I would much appreciate
correction if I am wrong.

We can model elliptical orbits with a Newtonian approximation at
moderate distances from the star, and in this case expansion has no
meaning beyond a change of coordinates. That seems fine.

But if we model a hyperbolic orbit then at some point the gravity of the
star becomes irrelevant, and the orbiting body moves into deep space, so
that Hubble expansion must become the dominant part of its motion. My
question is, How do we model such an orbit and where may I better study
it?




Regards

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Charles Francis
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Henning Makholm
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Joined: 19 Mar 2006
Posts: 7

PostPosted: Mon Jul 10, 2006 3:41 pm    Post subject: Re: Question about the path of a particle in Schwarzschild region of an cosmos Reply with quote

Scripsit Oh No <NotI@charlesfrancis.wanadoo.co.uk>

Quote:
As I understand it we can think of the Schwarzschild geometry
surrounding an isolated star as a static perturbation within an
expanding flat or near flat space-time.

...

Quote:
But if we model a hyperbolic orbit then at some point the gravity of the
star becomes irrelevant, and the orbiting body moves into deep space, so
that Hubble expansion must become the dominant part of its motion. My
question is, How do we model such an orbit and where may I better study
it?

The Schwarzschild metric does not include any Hubble expansion.
If you want to include that, you need to switch to a more realistic
cosmological model than "isolated star in an otherwise empty
universe". Which implies that you have to provide some positive
average matter density in the outer universe.

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Henning Makholm "I can get fat! I can sing!"
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Oh No
science forum addict


Joined: 06 Apr 2006
Posts: 82

PostPosted: Tue Jul 11, 2006 4:35 pm    Post subject: Re: Question about the path of a particle in Schwarzschild region of an cosmos Reply with quote

Thus spake Henning Makholm <henning@makholm.net>
Quote:
Scripsit Oh No <NotI@charlesfrancis.wanadoo.co.uk

As I understand it we can think of the Schwarzschild geometry
surrounding an isolated star as a static perturbation within an
expanding flat or near flat space-time.

..

But if we model a hyperbolic orbit then at some point the gravity of the
star becomes irrelevant, and the orbiting body moves into deep space, so
that Hubble expansion must become the dominant part of its motion. My
question is, How do we model such an orbit and where may I better study
it?

The Schwarzschild metric does not include any Hubble expansion.
If you want to include that, you need to switch to a more realistic
cosmological model than "isolated star in an otherwise empty
universe". Which implies that you have to provide some positive
average matter density in the outer universe.

Well, yes. That is the reason for my question. Unless I have overlooked

it, such a model is not given in any of my text books. The example I
gave was merely the simplest instance of such a model I could think of,
since it is perfectly possible to describe an empty flat expanding toy
universe. Just not one that obeys Friedman's equation.


Regards

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Charles Francis
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mark_horn@sbcglobal.net
science forum beginner


Joined: 18 Dec 2005
Posts: 6

PostPosted: Tue Jul 11, 2006 4:35 pm    Post subject: Re: Question about the path of a particle in Schwarzschild region of an cosmos Reply with quote

Oh No wrote:
Quote:
But if we model a hyperbolic orbit then at some point the gravity of the
star becomes irrelevant, and the orbiting body moves into deep space, so
that Hubble expansion must become the dominant part of its motion. My
question is, How do we model such an orbit and where may I better study
it?

I believe that, at the distances where the Hubble expansion becomes
significant, a solar system is (presumably) still bound within a
galaxy, so the expansion velocity is always irrelevant, wrt to your
orbiting mass. Beyond that I think you need to consider things like
large-scale bulk flow of whole galaxies in the streaming motion of
clusters; the CMB dipole anisotropy etc. (see e.g. Lauer and Portman,
APJ 425:418-438, 1994 April and Hudson et al APJ 512:70-82, 1999).

Cheers,
mark jonathan horn
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Greg Egan
science forum addict


Joined: 01 May 2005
Posts: 75

PostPosted: Thu Jul 13, 2006 12:10 am    Post subject: Re: Question about the path of a particle in Schwarzschild region of an cosmos Reply with quote

Oh No wrote:
Quote:
As I understand it we can think of the Schwarzschild geometry
surrounding an isolated star as a static perturbation within an
expanding flat or near flat space-time. I would much appreciate
correction if I am wrong.

We can model elliptical orbits with a Newtonian approximation at
moderate distances from the star, and in this case expansion has no
meaning beyond a change of coordinates. That seems fine.

But if we model a hyperbolic orbit then at some point the gravity of the
star becomes irrelevant, and the orbiting body moves into deep space, so
that Hubble expansion must become the dominant part of its motion. My
question is, How do we model such an orbit and where may I better study
it?

How about studying the Schwarzschild-de Sitter solution, which is an
exact vacuum solution where the expansion is due to a cosmological
constant?

I'm afraid I personally know nothing about this solution, but I expect
people have worked it all out in great detail.
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Oh No
science forum addict


Joined: 06 Apr 2006
Posts: 82

PostPosted: Thu Jul 13, 2006 12:39 pm    Post subject: Re: Question about the path of a particle in Schwarzschild region of an cosmos Reply with quote

Thus spake Greg Egan <gregegan@netspace.net.au>
Quote:
Oh No wrote:
As I understand it we can think of the Schwarzschild geometry
surrounding an isolated star as a static perturbation within an
expanding flat or near flat space-time. I would much appreciate
correction if I am wrong.

We can model elliptical orbits with a Newtonian approximation at
moderate distances from the star, and in this case expansion has no
meaning beyond a change of coordinates. That seems fine.

But if we model a hyperbolic orbit then at some point the gravity of the
star becomes irrelevant, and the orbiting body moves into deep space, so
that Hubble expansion must become the dominant part of its motion. My
question is, How do we model such an orbit and where may I better study
it?

How about studying the Schwarzschild-de Sitter solution, which is an
exact vacuum solution where the expansion is due to a cosmological
constant?

Thanks. That does not seem like a bad starting point.
Quote:

I'm afraid I personally know nothing about this solution, but I expect
people have worked it all out in great detail.

Yes, a quick glance at recent literature shows it has attracted

attention since the advent of the concordance cosmology, though I will
need to start with papers written about 1918 I think.


Regards

--
Charles Francis
substitute charles for NotI to email
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