Can you suggest any science fair projects that have to do with black holes?
Here's one you might be interested in that has to do with black hole
evaporation.
Stephen Hawking discovered from theoretical considerations back in the mid
1970's that black holes evaporate due to a quantum mechanical process.
The particular equations are as follows:
The black hole radius of its event horizon is given by
2 G M 28
R =  = 1.48 x 10 centimeters
2
c
The temperature of a black hole due to the emitted radiation is given by
3 26
h c 1.2 x 10
T =  =  Kelvins
8 pi G k M M
Equivalent mass of the radiation at this temperature
k T 37
m =  = 1.53 x 10 grams
2
c
The power radiated by the black hole, that is, its luminosity, is
40
2 4 10
P = 4 pi R A T =  Watts
2
M
The rate at which it looses mass is then
26
dM P 10
 =  =  grams per second
dt 2 2
c M
And the lifetime of the black hole undergoing evaporation is then
M 26 3
L =  = 10 M seconds
dM/dt
In the above formulae, M is the mass of the black hole in grams, and all
other constants are given in 'centimetergramseconds' units .c is the speed
of light ( 3 x 10^10 centimeters/sec), G is the constant of gravity
( 6.6 x 10^8 dynes cm^2/gram), A is the Stephan Boltzman constant ( 5.67 x
10^5 erg/cm^2/degree^4/sec), pi = 3.14159 and k is Boltzman's constant (1.38
x 10^16 ergs/degree).
First, use these formula to examine the properties of a variety of black holes
with masses from 10^5 grams ( quantum black holes), 10^14 grams ( miniblack
holes), 10^33 grams ( solar black holes) and 10^42 grams ( supermassive black
holes).
Physicists have predicted that at the Big Bang, black holes with sizes from
10^5 grams up to perhaps solar mass size might have been formed. Use the
above formulae to predict the mass range of the black holes would have lasted
as long as the present age of the universe, between 9 billion to 15 billion
years, and which should just now be evaporating completely away.
Predict what the final few thousand years of life would look like for such
black holes, by computing their REMAINING mass, the temperature of the
radiation they are producing, and their power.
From the equivalent mass of the emitted radiation, and the masses of various
fundamental particles such as electrons, protons, muons etc, predict the
kinds of particles that might be emitted by the black hole.
How bright would these evaporating black holes be compared to the SUn which
produces 3.8 x 10^27 watts of power? ( 1 watt = 10^7 ergs/sec).
As an astronomer, what would you look for in the sky that might be a candidate
for such a phenomenon? Examine the internet for information about
variable stars, supernovae, novae, flair stars, xray bursts and gammaray
bursts to find possible classes of phenomena, and discuss each one given what
you now know about evaporating black holes.
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