dstebbins Posted June 4, 2007 Share Posted June 4, 2007 Wikipedia lacks an article about black hole entropy, so I'm going to try and work it out for myself. I want you guys to help me by correcting mistakes and answering questions. It is my understanding that "entropy" is quantum mechanics talk for "information/description." So basically, when Stephen Hawking came up with the famous equation of S = (c^3*k*A)/(4*h*G), (h is actually read "h-bar," but I don't know how to type the real letter) he combined all the possible information of a black hole into one value, which he assigned the capital letter S. The units for the variables are thus: c^3=m^3/s^3, since c is the speed of light and thus is a velocity. k=J/K, or Joules per Kelvin, h=Js, or Joule seconds, and G=Nm^2/kg^2, read "Newtons meters squared per kilograms squared," and A=m^2, since it's merely surface area. Therefore, when I figure the units on the right side, cancelling where appropriate, I get a unit for S of S=(m^3*kg^2)/(s^2*K*N). Since the only variable on the right side of Hawking's equation that is not a constant is A, or surface area, then I feel it is safe to assume that all black holes of equal size are the same. The values of the constants are as follows: c=299792458 m/s k=1.3806504 x 10^-23 J/K h=1.054571628 x 10 ^-34 Js G=6.67428 x 10^-11 Nm^2/kg^2 As I calculate the constants in my calculator, with the proper number of significant digits being 6, I get a final unitless value of 1.32131 x 10^46, so that means that the entropy of a lack hole is S=(1.32131 x 10^46)A (m^3*kg^2)/(s^2*K*N*m^2) And with that, I come to my final belief, that the singularity paradox is brought to life because the singularity is infinately small, and thus has no surface area, so A=0, so you're multiplying 1.32131 x 10^46 times 0, and you get zero, so at the singularity, there is no entropy. I know my logic is probably plagued with flaws (it always is), so I'd appreciate it if you could correct my mistakes and answer any questions I may have in the process. Link to comment Share on other sites More sharing options...

lakmilis Posted June 5, 2007 Share Posted June 5, 2007 well, I am very unsure about the topic of entropy. I never felt comfortable with accepting current definitions and interpretations. So only thing I wanted to point out is that when you state black hole entropy and stating there is none at the singularity, it makes sense as such. There are two solutions for a black hole, the event horizon and the singularity. At the singularity absolutely all physical meaning from our models and theories break down, thus finding 0 as an answer is no surprise (an infinite value wouldn't be a surprise either really). I think though the entropy of a black hole has more to do around the EH. Black holes at the EH have technically a surface area and that is what the entropy is related to I believe. Adding the cosmic censorship principle makes entropy at the singularity with that in mind, irrelevant (thus 0 is quite sensical, so would a indetermined value of [MATH] infinity [/MATH] Link to comment Share on other sites More sharing options...

dstebbins Posted June 5, 2007 Author Share Posted June 5, 2007 Nevermind. I learned on another board I posted this that I had a misguided definition of entropy in the first place. Entropy is actually a measure of an objects tendancy to take on a trait uniform with its surroundings. In thermodynamics, entropy refers to a substance's tendency to reach the same temperature as its environment. So it's back to square one. You can all delete this topic now. Link to comment Share on other sites More sharing options...

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