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Re: value of g in black holes



On Wed, 17 Oct 2001, Carl E. Mungan wrote:

Since no one else answered, I toss out the following. It's not GR so
it's probably wrong (I'm no expert), but at least it's digestible by
first-year students:

escape velocity c = sqrt(2GM/R) where M and R are mass and radius of black hole

g = GM/R^2

Solve first equation for R, plug into second.
Minimum mass of black hole is 3 solar masses. Maximum mass of known
stars is something like 30 solar masses.

Hence, we find that g can range from about 0.5 to 5 in units of
Tm/s^2. This is the value of g at the event horizon *after* the black
hole has formed.

It is thought that 10^8 or more solar mass black holes exist in
the center of some galaxies. A 10^8 solar mass black hole would
have R = 1000 light seconds and g = 150 km/s^2 at the event
horizon.

The universe might have something like 10^22 to 10^24 (give or
take a few factors of ten) star's worth of mass. If 10^24 solar
masses were to coalesce into a black hole (or simply already and
for all time have been a black hole), R would be billions of light
years (i.e., something like the size of the universe) and g would
be 15 pm/s^2 (i.e., completely negliglbe) at the "event horizon."
Interesting?

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm