From: baez@galaxy.ucr.edu (John Baez)
Subject: Re: Expansion of the Universe and Ionization
Date: 11 Aug 2000 22:12:44 GMT
Newsgroups: sci.physics.relativity,sci.physics.research
Summary: [missing]

In article <nuNk5.231087$t91.2205450@news4.giganews.com>,
Paul Lutus <nospam@nosite.com> wrote:

>Ted Bunn wrote:

>> If the Universe keeps expanding forever, then the probability is
>> essentially zero.  Black holes in different galaxy clusters are
>> currently moving away from each other due to the expansion,

>This is a common misconception about universal expansion. The universe is
>expanding, but this does not mean individual galaxies, or even clusters of
>galaxies, are also expanding. They are gravitationally bound. Therefore as
>time passes there is plenty of opportunity for black holes to merge within
>or between galaxies.

Despite your reference to "misconceptions", nothing you wrote 
contradicts what Ted said.   He explicitly referred to black holes 
in DIFFERENT GALAXY CLUSTERS.   While individual clusters are 
gravitationally bound, different clusters move away from each other.  

This sets an upper limit on how big black holes will get: the mass
of a cluster is about 10^14 solar masses, so we can't expect black
holes to get bigger than that.

But this is probably an extreme overestimate.  Even though galaxies 
and clusters are "gravitationally bound" in the technical sense of 
having total negative potential energy exceeding the total positive 
kinetic energy (in the Newtonian approximation), individual stars 
will still "boil off" as time progresses, thanks to randomly managing
to acquire enough kinetic energy to achieve escape velocity.   

People have done computer simulations of this process.  And in the long 
run (about 10^19 years) it's estimated that about 90% the stars will boil 
off the galaxies in this manner.  Of these, I suspect a hefty fraction 
will also boil off the clusters (the timescale being about 10^23 years).
These stars are unlikely to fall into black holes.

For the same reason, we can't expect all the black holes in a given
cluster to form a single humongous black hole.   Many will boil off.

In brief: some stuff falls down, but the resulting decrease in potential 
energy means that *other* stuff must get a lot of kinetic energy and shoot
off.   These two processes are inseparable.