From: Jeff L Jones (jeff@spoonless.net)
Date: Sat Aug 25 2007 - 14:40:18 MDT
I get:
mass of sun = 2*10^30 kg
total energy in observable universe ~ 10^55 kg ~ 10^25 suns
radius of observable universe = 78 billion lightyears = 7*10^23 km
Schwarzschild radius of observable universe = 3*10^25 km
So it looks like, just based on the usual linear scaling of
Schwarzshild radius with mass, one would think our universe would be
in a black hole with a radius about 42 times the current observable
horizon. Interesting that they are so close (less than 2 orders of
magnitudes away)... I'm not sure why.
However, I don't think you can apply the usual relationship between
mass and Schwarzschild radius to the universe as a whole. Several
reasons I can thnk of why it probably shouldn't apply: 1.) we've
measured the universe to be approximately flat... if it were a black
hole, it should be highly curved, 2.) it's expanding, which makes the
geometry different from a usual black hole, and 3.) the dark energy is
exerting negative pressure (that is, outward pressure) which might be
another way of understanding what's keeping it from collapsing into a
black hole.
I think the formula for calculating Schwarzschild radius in terms of
mass is a useful rule of thumb, but you have to look at more than that
to actually see if you get a real black hole.
Jeff
On 8/25/07, Thomas Buckner <tcbevolver@yahoo.com> wrote:
> I read the suggestion that our universe could
> itself be a black hole years ago (might have been
> Sagan). It made sense and still does.
> Functionally there is no difference between the
> impossibility of visiting other universes
> (different inflationary bubbles or what have you)
> and the impossibility of communicating out of a
> black hole with the surrounding regions. The wiki
> entry
> http://en.wikipedia.org/wiki/Schwarzschild_radius
> Explains the idea succinctly:
>
> "A classification of black holes by mass:
>
> micro black hole and extra-dimensional black hole
> primordial black hole, a hypothetical leftover of
> the Big Bang
>
> stellar black hole, which could either be a
> static black hole or a rotating black hole
>
> supermassive black hole, which could also either
> be a static black hole or a rotating black hole
>
> visible universe, if its density is the critical
> density"
>
> You see, it is permissible to have a
> Schwarzschild radius of tens of light years given
> the amount of mass our Hubble radius may contain,
> and still feel perfectly at home in it! From wiki
> on "Event Horizon": "The Schwarzschild radius of
> an object is proportional to the mass. For the
> mass of the Sun it is approximately 3 km, and for
> that of the Earth about 9 mm." The Sun has about
> 333k times the mass of Earth and, it would seem,
> about 333k times the Schwarzchild radius. I
> calculate (from wikipedia sources) that the
> universe has a mass of about 15 quintillion Suns.
> It seems it should have a Schwarzchild radius of
> some 303 septillion kilometers, but the
> observable universe has a radius of 435
> quintillion kilometers.
>
> Unless I've bollixed my estimates, our universe
> has a Schwarzchild radius almost 700k times
> farther off than its visible edge. Hence: black
> hole.
>
> Tom Buckner
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