Analysis of Functions

Analysis of Functions

Review of Functions
Mass
Luminosity
Energy
Temperature
Schwartzchild Radius

In the last two sections we derived formulas for mass, luminosity, energy, temperature and Schwarzchild Radius. Now lets look at graphs of these functions and see what those functions really tell us.

Mass vs. Time
	Using this graphical representation of the function we can see that the function tells us that the blackhole loses mass through Hawking Radiation increasingly as time approaches the evaporation time (ie t=0).
Luminosity vs Time
	The luminosity of the blackhole is very faint during its infancy. But as t approaches zero the blackhole's luminosity through Hawking Radiation increases greatly. Also we can note that the luminosity of the blackhole near the end of its existance is infinite. However, the luminosity is only infinite for a very small period of time because of the growth of this function.
Energy vs Time
	The energy released by a blackhole interestingly decreases as it approaches the final evaporation point. This probably has to do with the fact that the blackhole loses mass and since it has a smaller radius due to smaller mass it does not have as great of a surface area to release as much energy as it did in its earlier existance.
Temperature vs Time
	The temperature of a blackhole increases as it becomes older. The temperature also increases greatly as the blackhole ages. Since the temperature seems to flatten out considerably when it is very young it almost appears as if the temperature will never reach "ordinary" temperatures because of the Hawking Radiation.
Schwartzchild Radius vs Time
	Just like the mass (which makes sense because of the close relationship between the two) the Schwarzchild Radius of the blackhole decreases as it approaches evaporation (t=0). Also the decrease in radius increases as the blackhole becomes closer to the ending of its existance.