physics question #2892

Yevgeniy Perev, a 20 year old male from Staten Island asks on August 30, 2005,

Q:

How much energy in joules will be produced from an exploding mini black hole that is 10 micrograms in mass?

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Werner Israel answered on August 31, 2005, A:

This is a fascinating question! It has a short answer and a long answer. The short answer is just Einstein's E= Mc^2. Since 10 micrograms = 10^(-5) gm and c= 3 x 10^10 cm/sec and 1 cal=4.18 joules with 1 joule = 10^7 ergs, the answer is E= (10^ (-5) x (3x10^10)^2 / 4x10^7. I make it roughly 200 million calories which = 900 million joules.

Why would it explode? A black hole of this mass is very hot--having a temperature of about 10^32 degrees centigrade! It evaporates almost instantly in a flash of Hawking radiation.

There is something special about the mass of 10 micrograms quoted by Mr. Perev. This black hole is very tiny. It would have a diameter of 10^(-33) cm. In this domain, the contest between the opposing forces of gravity--the clumping tendency of matter, proportional to mass--and quantum physics--the waviness or fuzziness of particles, inversely proportional to mass--is just about even. Ten micrograms is the smallest black hole that can form. Below this mass, matter is too fuzzy and gravity is too weak to form black holes. Ten micrograms and 10^(-33) cm are natural units for quantum gravity. They are called Planck units.

In the 1970's, Hawking speculated about possible mini-blackholes (about the mass of a mountain) which might have formed early in the big bang. Such black holes would now be in the last stages of evaporation, and would finally disappear in a 200 million Joule explosion. He thought this might explain the then still very mysterious gamma-ray bursts. However, it is now accepted that this explanation won't work--it doesn't agree with observation.