Visible Horizons

From: "Jonathan Thornburg [remove -animal to reply]"
Subject: Visible Horizons
Newsgroups: sci.astro.research
References:

WG wrote:
Visible Horizons as Gravitational Potential Wells
[[Newtonian calculation of cosmological gravitational redshift]]
We can do a quick back of the envelope Newtonian calculation to see
if we are at least in the right Ball Park.
[[...]]

The problem with this calculation is that it's Newtonian, i.e.,
it assumes that we can neglect the overall curvature of spacetime.
[If you want to get into more detail, the theorem
that "you can ignore the effects of spherically
symmetric matter outside the observer" doesn't hold
in curved spacetimes.]
But on cosmological scales, that curvature matters a lot, so you
need to use general relativity (or some other relativistic theory
of gravity if you prefer) to get reasonable results. And when you
redo the particular calculation here using general relativity (with
a reasonable cosmolgical model), you find no gravitational redshift
for distant objects, just the usual expansion-of-the-universe redshift.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"C++ is to programming as sex is to reproduction. Better ways might
technically exist but they're not nearly as much fun." -- Nikolai Irgens

Jonathan Thornburg wrote:
WG wrote:
Visible Horizons as Gravitational Potential Wells
[[Newtonian calculation of cosmological gravitational redshift]]
We can do a quick back of the envelope Newtonian calculation to see
if we are at least in the right Ball Park.
[[...]]

The problem with this calculation is that it's Newtonian, i.e.,
it assumes that we can neglect the overall curvature of spacetime.
[If you want to get into more detail, the theorem
that "you can ignore the effects of spherically
symmetric matter outside the observer" doesn't hold
in curved spacetimes.]
But on cosmological scales, that curvature matters a lot, so you
need to use general relativity (or some other relativistic theory
of gravity if you prefer) to get reasonable results.

There is a GR formula building the Schwarzschild geometry at:
http://en.wikipedia.org/wiki/Redshif...ional_redshift
http://en.wikipedia.org/wiki/Gravitational_redshift

And when you
redo the particular calculation here using general relativity (with
a reasonable cosmolgical model), you find no gravitational redshift
for distant objects, just the usual expansion-of-the-universe redshift.

The redshift sticks off to infinity at the Schwarzschild radius r_s
2GM/c^2. If this formula is applicable to a homogeneous universe with
density rho, there is such a finite r_s = c/sqrt(2G rho). (For small r,
the redshift is z = GM/(c^2 r) = G rho r^2.)

The question is though what density rho to use to compute the r_s. In
the past one would have assumed that most mass came from the lit matter.
But then one found it is just a small part of the galaxies, and
gravitational microlensing shows there is a lot of matter between the
galaxies as well.

But it would be interesting to know what values of r_s one gets for
different choices of rho (without first applying universe expansion models).

Hans