black hole entropy

[dstebbins]

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.

[lakmilis]

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]

[dstebbins]

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.