Calculating The Event Horizon of a Supermassive Black Hole

  1. Ok, lets say we wanted to know the diameter of the largest black hole. (Its event horizon) Lets say the universe had contracted and all the galaxies had been consumed by black holes and all merged into one single massive hole.

    Say there were approximately 100 billion galaxies, all relatively the same size, and each had an average of 200 billion solar masses. 1 solar mass = 1.9891 × 10^30 kilograms

    I believe the formula to calculate the radius of the event horizon is 2GM/c^2

    Not being very good with math, perhaps someone would be able to calculate this? Thanks in advance…
     
  2. jcsd
  3. I dont know much about black holes, but that equation you gave can be determined by knowing the mass of the black hole, since G and c are both constants. That bothers me a little, that you can calculate length from mass.
     
  4. pervect

    pervect 8,041
    Staff Emeritus
    Science Advisor

    Welcome to the wonderful world of geometric units, where time, length, mass, and even charge can all be expessed in terms of the same unit - usually, cm.

    G/c^2 is the conversion between mass and distance, this is most convenient in a unit system where G=c=1 :smile:

    The answer to the specific question asked previously is most easily found with Google's calculator. Just go to http://www.google.com and type in

    G*(100*10^9*200*10^9*2*10^30 kg)/c^2

    and the answer pops out, 3*10^25 meters

    If you want that in inches, you can say "in inches" at the end, and it will convert the answer to inches (1.1*10^27 inches).

    The "more about calculator" link gives more info on the calculator, if you type in any recognized mathematical expression (the above, or if you're having trouble, type in a simple mathematical expression, 2+2 will do it).
     
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