|MadSci Network: Physics|
That's a good question. There are of course different theories as to how one might determine such a quantity specifically for such an exotic object as a black hole. Some complex and some of them simple. I will direct you towards some straight forward answers as best I can. First, I can refer you to two books, which discuss several theories on black hole characteristics and some of the deeper questions which prevail. The two books touch on entropy, but I can tell you that they have no simple equations or formulas for such a calculation, but, nonetheless, could answer some of your questions and lead you in the right direction. The two books of which I speak are : "A Brief History of Time: From Big Bangs to Black Holes", by Stephen Hawking. "Cauldrons in the Cosmos: Nuclear Astrophysics", by Claus E. Rolfs and William S. Rodney. Having read both books, I found them to be very descriptive on several characteristics of stellar phenomena such as black holes, but are lacking in quantitative approaches of which you seem to seek. I also performed an in-depth search on the World Wide Web to find documentation or clarification on entropy determination for black holes. I began my search by looking for a scientist by the name of David Ward, since I had read some things he had to say about thermodynamics and black holes and found an excellent result which fits your request very well and should provide you with a very clear answer which provides you with explanations and a nice smooth guide through the calculation. The explanation is provided at the web site: members.aol.com/rebeccawrd/index.html and is entitled: "Black Holes and Thermodynamics: The Physics of Black Holes by David Ward" This explanation follows in the logic of there being a relation between the area of the event horizon and the total entropy of the black hole, which is explained in the Hawking book shown above. The theory goes that as an object falls into a black hole, the entropy of the surroundings goes down and the entropy of the black hole increases. This increase is thought to result in an increase in the area of the event horizon. The explanation provided by David Ward encompasses this and touches on several other useful concepts in the calculation, such as black-body radiation and the Schwartzschild radius, which are needed to arrive at the resulting entropy of the black hole in question. Well, I hope these resources guide you to your answer. Good luck.
Try the links in the MadSci Library for more information on Physics.