PhD comics and mini black holes

# PhD comics and mini black holes

The entire universe in blog form
Nov. 20 2007 10:14 AM

# PhD comics and mini black holes

The second part of the PhD comic strip I mentioned yesterday is out, and lots of astrobloggers are linking to it. But no one seems to have noticed the glaring error in it:

Phil Plait

Phil Plait writes Slate’s Bad Astronomy blog and is an astronomer, public speaker, science evangelizer, and author of Death From the Skies!

Black holes are at the center of a lot of misconceptions. Basically, they are objects where the escape velocity is greater than the speed of light. If you throw a rock straight up off the surface of the Earth, you must give it a velocity of 11 km/sec for it to be able to get away from the Earth and not fall back down*. That's because the Earth's escape velocity is 11kps. It depends on the size of the object and its mass, or, if you prefer just its density.

Black holes are so small and so massive (or just plain dense) that their escape velocity is faster than light. You literally cannot escape them once inside their ravenous maw. The size of a black hole is actually rather simple to calculate if you know its mass:

radius = 2 x G x mass / c2

G is Newton's Gravitational constant of the Universe, and is just a number. c is the speed of light. It turns out that for a star like the Sun, it would have to be crushed to a diameter of about 6 kilometers to becomes a black hole. But look at the equation! If I double the mass, the size of the black hole doubles. So it's really easy to scale this equation to different mass black holes.

The one in the center of the Milky Way Galaxy has a mass of roughly 4 million times the Sun's mass, so it must be 4 million times bigger, or 24 million kilometers across, far less than the distance between the Sun and Mercury (for comparison, the Sun is about 1.4 million kilometers across right now).

Black holes are small.

However, they can get even smaller. There is a hypothesis that just after the Big Bang, fluctuations in the density of matter may have compressed small amounts of material so much they collapsed into black holes. These are called mini black holes. If you plug in the mass of, say, a typical mountain or asteroid into the equation above, you'll see that a mini black hole is actually far smaller than an atom!

I won't even go into Hawking radiation, which says that a black hole that small would have a surface temperature of 10 billion Kelvins. That would make them a bit obvious if they were pelting us; they'd be pretty bright.