### Saved science fair projects:

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### 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 'centimeter-gram-seconds' 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 ( mini-black 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, x-ray bursts and gamma-ray bursts to find possible classes of phenomena, and discuss each one given what you now know about evaporating black holes.