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The Hawking wattage of a black hole

  1. 0.36 nanowatts

    1 vote(s)
    100.0%
  2. 0.36 microwatts

    0 vote(s)
    0.0%
  3. 0.36 milliwatts

    0 vote(s)
    0.0%
  4. 0.36 watts

    0 vote(s)
    0.0%
  1. May 15, 2003 #1

    marcus

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    Assume the surface area of the event horizon of an ordinary black hole is 1050,
    ordinary meaning uncharged and nonrotating.
    The hole glows with Hawking radiation----what is the radiant power?


    I gave the event horizon area in natural units but it's easy to convert to square meters if you wish it that way.
    The area 1050 is 2.6 x 10-20 square meters, or 2.6 square angstroms.

    In natural units (c=G=hbar=k=1) the radiant power of a BH
    with area A is simply

    1/960A

    So having the area 1050 means that the luminosity is essentially 10-53. To which of the four wattage figures given in the poll is this equivalent?
     
  2. jcsd
  3. May 16, 2003 #2
    For some reason I'm getting 1.0110686E-103 for the radiant power...is this right?
     
  4. May 16, 2003 #3

    marcus

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    Could you have squared the area by mistake?

    the area is E50 in planck units
    the formula for the overall power is 1/960A

    so you should take reciprocal of 960E50
    and it comes to about 1.04E-53 in units of planck power

    Planck power (c5/G) is an awesome amount of power.
    It could supply the mass-energy of a whole galaxy in a few days.
    You can easily calculate what it is in watts, if you look up the metric system values for G and c. It is around 3.6E52 watts---you can easily check this.

    WAIT! Kyle you have calculated the radiant power PER UNIT AREA approximately correctly!!!! The total power from the whole ball (namely 1.04E-53) divided by the area of the ball (namely E50) is indeed 1.04E-103.

    Bravo Kyle! And thank you for responding.
     
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