Science Forums 2

[CraigD]

Originally Posted by Hasanuddin

What is the smallest sized possible black-hole?

Assuming that the quantum mechanical prediction of Hawking radiation is correct, the lifetime of a black hole into which no matter or EM radiation is infalling is exactly proportional to the cube of its mass. Specifically:



With this, and reasonable assumptions about typical rates of radiation and infalling matter, you can calculate the mass of a black hole of various short lifetimes. For example, a kg black hole has a lifetime of about 1 second, a kg one about 1 year, and a kg one about s, about the current age of the universe according to Big Bang model. By way of comparison, kg is just a bit more than the mass of a large artificial structure like the Three Gorges Dam.

In principle, a small black hole could be stable – that is, be at equilibrium, neither gaining nor losing mass – if the power of its infalling matter and radiation equals that of its Hawking radiation. For the cosmic background radiation – which all objects are more or less guaranteed to receive – a black hole of about kg – about the mass of Earth’s moon has about this equilibrium.

In principle, an arbitrarily small black hole could be stable if it received a arbitrarily large amount of EM radiation (infalling matter couldn’t be used to stabilize an arbitrarily small black hole, because the exclusion principle limits the amount of fermionic mater that can occupy a given volume of space.)

Even though the first of these scenarios is easily imaginable, neither has been observed, nor is a compelling scenario that could result in either occurring been described in any literature of which I’m acquainted.

Originally Posted by Hasanuddin

And what are the implications of the answer to this question?