OK, I did some calculations and came up with some interesting results. According to my theory, you have to take into account the random, thermal movement of atoms when the mBH is at rest with respect to the center of the Earth. So modifying
Casadio et al.'s formula dM/dt =
π*v*
ρ*R
2 to:
dM/dt = 4*π*v*ρ*R2
since the mBH will have molecules vibrating at it coming from all directions, we have to use the area of a sphere, rather than the cross-section, to calculate the accretion rate.
Now, going off of Casadio et al.'s (CFH) Table II, for the values M
c (the critical mass an mBH needs to go 4-D--I think) = 10
6 kg and 10
7 kg(the second and third lines, respectively). The chart shows the maximum masses mBH's would have under CHF's theory for various values of M
c, along with other parameters like the effective capture radius (R
EM).
Thus, one can calculate roughly the evaporation rate by dividing the maximum mass by the life expectancy. I can now calculate the accretion rate, where I assume v (the average thermal velocity of the surrounding iron atoms) = 2500 m s
-1 and
ρ = 13,000 kg m
-3 (R = 1.6 x 10
-16 m and 2 x 10
-15 m, respectively):
Code:
for Mc = 106, the evaporation rate is 2.9 x 10-21 kg s-1
for Mc = 106, the accretion rate is 1.6 x 10-22 kg s-1
for Mc = 107, the evaporation rate is 2.7 x 10-22 kg s-1
for Mc = 107, the accretion rate is 1.6 x 10-21 kg s-1
As you can see, for the latter case, the accretion rate exceeds the evaporation rate. Thus, it
does seem possible than an mBH could grow to catastrophic sizes. That's potentially problematic.
