Question

Suppose black holes radiate their mass away and the lifetime of a black hole created by a supernova is about \({\rm{1}}{{\rm{0}}^{{\rm{67}}}}\)years. How does this lifetime compare with the accepted age of the universe? Is it surprising that we do not observe the predicted characteristic radiation?

Short answer

The lifetime of a black hole is \({\rm{1}}{{\rm{0}}^{{\rm{67}}}}\) times greater than the age of the universe, which makes it no surprise that the radiation has not yet been observed.

Step-by-step solution

Existence of black hole

The existence of black holes, objects for which the escape velocity is greater than the speed of light and from which nothing can escape.

Comparing the lifetime of black hole with accepted age of the universe.

The age of the universe is around \({\rm{1}}{{\rm{0}}^{{\rm{10}}}}\)years. The expected lifetime of a black hole is \({\rm{1}}{{\rm{0}}^{{\rm{57}}}}\) times greater than the age of the universe! Because of this much greater lifetime, it is not surprising that the characteristic radiation has not yet been observed.