Calculating The Event Horizon of a Supermassive Black Hole

[Vast]

Ok, let's say we wanted to know the diameter of the largest black hole. (Its event horizon) Let's 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…

 

[ArmoSkater87]

I don't 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.

 

[pervect]

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

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).