The Size of a Black Hole

Until people understand what black holes are, some have the impresson that they suddenly become giant, super strong sucking machines that eat anything and everything in the vacinity. This is only part of the picture. To get a better picture, I want to consider the size of a black hole. Technically, the black hole itself is a point; not a dot, like the period at the end of a sentance, but a point, with no size (even an atom has size). What we mean by the size of a black hole is something called the Schwartzchild Radius. I will explain this momentarily. For now, notice that it is very small.

 

Table: The size of some objects when crushed to black hole size. This numbers need to be redone; I am including them from memory. Notice that an atom has a diameter of about $1\times 10^{-10}\,{\rm m}$. A person-mass black hole has smaller than 10^-20, which is as much smaller than an atom than an atom is smaller than a person. 10^-25 is an additional 10,000 times smaller than this.

Object	Mass	Normal Radius	Black Hole Radius
Sun			$3\,{\rm km}$
Earth			$1\,{\rm cm}$
Moon			$0.1\,{\rm mm}$
Person	$80\,{\rm kg}$	$2\,{\rm m}$	$2\times 10^{-25}\,{\rm m}$

Think about crushing the Earth down to a $2\,{\rm centimeter}$ diameter ball.

The black hole formed from the Earth would have the same mass as the Earth. If you were a distance equal to the radius of the earth from this black hole and you dropped something, it would still fall at a rate of $9.81\mbox{$\phantom{1\!}^{{\rm m}\!\!}/_{\!\!{\rm s^2}}$ }$. That is to say, as long as you stay further away than the original radius of the Earth, you would not notice a difference. Well, except that there would be no surface of the Earth underfoot. It is only when you get very close to the black hole that you notice the amazing strength of gravity. That is the peculiar feature of black holes, that you can get extrememly close. Recall that the force of gravity is calculated by $$F = G \frac{M m}{R^2}$$. Usually, R is necessarily larger than the radius of the body. In the case of a black hole, you can get arbitrarily close. As R gets really small $(R \rightarrow 0)$, the force gets really big $(F \rightarrow \infty)$.