1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Entropy of a Schwarzchild black hole

  1. May 2, 2005 #1
    Hi, i'm looking for some help on where to start with this question:

    The surface area of a Schwarzchild black hole is [tex]A=16 \pi R^2_c[/tex] where [tex]R_c[/tex] is the distance of the event horizon from the centre of the black hole. Show that for such a hole containing quantized matter, its entropy can be written

    [tex]S = \frac{\xi k c}{4\pi h G}A[/tex]

    where [tex]\xi[/tex] is a numerical constant.



    I know that the enropy of a change is

    [tex]S = \int_{initial}^{final} \frac{Q_{rev}}{T}[/tex]

    and can show that using the de Broglie relation

    [tex]\lambda dB <= 2R_c = \frac{4GM}{c^2}[/tex]

    the energy is

    [tex]\frac{hc^3}{4GM} <= E[/tex]

    But i'm not sure where to go with proving that the entropy is the equation given.
     
    Last edited: May 2, 2005
  2. jcsd
  3. May 2, 2005 #2
    It looks like you got your Latex wrong. Change the [\tex] to [/tex].
     
  4. May 2, 2005 #3

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    [tex] S_{Beckenstein-Hawking}=\frac{A}{4\hbar} [/tex]

    is more likely defined...

    Daniel.
     
    Last edited: May 2, 2005
  5. May 2, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    In the section 12.5 of his book [1],Wald shows that the first law of thermodynamics for a black hole can be written

    [tex] dM=\frac{1}{8\pi}\kappa dA+\Omega_{H}dJ [/tex]

    Daniel.

    ----------------------------------------
    [1]Wald R.M."General Relativity",1984.
     
  6. May 2, 2005 #5
    Ok, thats helpful, thanks. I assume [tex]\Omega_{H}dJ [/tex] represents work done.

    Does that mean the two forms

    [tex] dM = \frac{K dA}{8\pi} + work[/tex]
    [tex]dE = T dS + work[/tex]

    could be equated?

    [tex]dE - T dS = dM - \frac{K dA}{8\pi}[/tex]
     
    Last edited: May 2, 2005
  7. May 2, 2005 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Yes,[tex] TdS=\frac{1}{8\pi}\kappa dA [/tex]

    Daniel.
     
  8. May 2, 2005 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    And one more thing,it's Karl Schwarzschild.

    Daniel.
     
  9. May 2, 2005 #8
    Thanks for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Entropy of a Schwarzchild black hole
  1. Black hole (Replies: 1)

  2. Miniture Black holes! (Replies: 4)

Loading...