Re: value of g in black holes

["Carl E. Mungan" <mungan@USNA.EDU>]

Dwight asked:

>     I'm currently going over gravitational forces and acceleration
> with my first
> year physics students.  Of course, one of the topics that the students' had
> brought up were black holes.  One of the questions, I didn't know
> and haven't been
> able to find the answer...so I'm coming to the experts!  :)  What must be the
> value of g (in m/s/s) so that a "black hole" would form?

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.

If you instead wanted the value of g *before* formation, then replace
the first equation above with the fact that stellar radius is
approximately linearly proportional to stellar mass (eg. Chaisson &
McMillan "Astronomy Today" Fig. 17.22). So we have something like R =
M (both in solar units). Hence g varies from about g_sun/30 to
g_sun/3, which turns out to be about 1 to 10 g_earth.

HTH, Carl
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/