Fun Fact - A Red Black Hole

As described earlier, a black hole evaporates by emitting hawking radiation. Massive black holes are cold, emitting little radiation, while micro black holes are blazing hot, and evaporate in a flash. In either case, matter is converted into energy with perfect efficiency. Given enough time, all the mass of the black hole becomes energy, as per e = mc2. The only other system that attains 100% efficiency is a matter antimatter annihilation. An electron + a positron yields two gama ray photons flying apart in opposite directions (thus conserving linear momentum), each with an energy equal to the rest mass of the electron or positron, 511 keV. Perhaps an evaporating black hole, constructed by us or found naturally in the galaxy, could serve as a power source for a space ship, a space station, a fledgling colony, or our descendants after the stars have all burned out.

The ideal temperature for harvesting power is red hot, about 1,500 degrees C. what kind of black hole has this temperature? It's mass lies somewhere between the super massive black hole at the center of our galaxy, with a temperature near absolute zero, and a fleeting micro black hole that flashes away in a gamma ray burst.

A black hole having the mass of the moon, 4.5E22 kg, has a diameter of 13 micrometers and a temperature of 2.7 kelvin, which is the same as the cosmic microwave background. If such was adrift in interstellar space it would emit as much radiation as it absorbs, and remain stable. It would neither shrink nor grow. To make a red hot black hole, divide the mass by 500, thus multiplying its temperature by 500. The diameter is now 26 nanometers, the size of a large molecule or a small virus. It glows red, but could you even see it? Perhaps, against the blackness of space.

Compare our supposed red black hole with Betelgeuse, one of the few red stars in the sky. Having an apparent magnitude of 1, (with some variations), Betelgeuse is the eighth brightest star in the night sky. It's angular diameter, barely measurable with today's technology, is 0.05 arcseconds. To look as bright as Betelgeuse, our black hole has to have the same angular diameter. Multiply 20 × 3600 × 360, and Betelgeuse accounts for 1 / 25920000 of our circle of visibility. Multiply this by 26 nanometers to find a circle whose circumference is 0.67 meters. You must stand 10 centimeters (4 inches) from the black hole to see it as a bright red star in the sky. As we'll see below, this is a very dangerous proximity.

Power and light go hand in hand. Betelgeuse doesn't keep you warm on a cold winter's night, and the power of this black hole, even 10 cm away, is negligible. Black holes can't provide steady reliable power, because they are either too cold or too small. Still, they are scientifically interesting, so let's continue to explore.

Ten centimeters is just too close, can we see it from farther away? In the darkness of space, young eyes can see objects 100 times fainter than Betelgeuse, down to magnitude 6. That pulls you back to a meter, which is still too close. From any safe distance, this microscopic red dot is invisible.

On the surface of the moon, gravity is 1/6. Divide the moon's mass by 500, and gravity is 1/3000. Compress this mass down to a point, but remain where you are, 1,737 km away from the center, and gravity is still 1/3000. Convert this to a formula for gravitational force in G's as a function of distance from the red black hole.

f = 1000 / d2 (kilometers)

f = 1E9 / d2 (meters)

Stand one kilometer away from the black hole, and you are being pulled in with a force of 1,000 G's. If, by some miracle, your space station is able to hold its position, you will be crushed flat against the floor, as thin as a piece of paper. If the station cannot hold its position, then you are falling, and falling fast! At a distance of one meter, when you can finally see the red dot that is dragging you to your death, the force is a billion G's. But something interesting happens before then. Suppose you are falling feet first into the black hole. When your feet are at 800 meters the gravity pulling them down is 1562 G's. However, the gravity at your head, at 802 meters, is 1554 G's. That's a difference of 8 G's, pulling your body apart like a medieval rack. This is enough force to dislocate your joints. By 600 meters the difference is 18 G's, enough to tear your legs and arms off your body. At 100 meters, tidal forces pull individual fragments of muscle, skin, and organs into long thin strips. This process is called spaghettification, turning everything into long strands of spaghetti. Obviously this is not pleasant.

One way to hold your position a kilometer away from the black hole is to assume a circular orbit. Inward acceleration is 10,000 meters per second squared, and this must be balanced by v2/1000. Your space ship must whizz around the circle once every 2 seconds. don't look out at the stars; you might get dizzy. And there's still the problem of the tides. If the floor of your ship is 2 meters below its center of mass, you will experience 4 G's lying on the floor. If the ceiling is 2 meters above the center of mass then another 4 G's pulls objects towards the ceiling. 4 G's is survivable for a time, but rather unpleasant, and it would probably tear your space ship apart. tidal forces are inversely related to distance cubed, so you should be at least 10 kilometers away from the black hole if you want to maintain an orbit. Opposite ends of your space ship will experience a few hundredths of a G, depending on the size of your ship, and that is probably manageable.

What if you drop something inanimate into the black hole, something you don't particularly care about, like a grain of sand. If you're in orbit around the black hole and you release a grain of sand it will remain in orbit with you. Instead, you must decelerate the grain of sand so that it has no angular velocity. It is essentially hovering above the black hole, ready to fall into the hungry red dot. If the grain still has some forward velocity, it might trace a new orbit, a long thin ellipse that flies down to the black hole, whips around it at close range, then swings back up to its highest point. Too close, and the grain of sand is pulled apart by tidal forces. In a field of a billion G's, one meter away from the black hole, this is possible. But there is something else to consider. Near a black hole, Newton's elliptical orbits no longer apply. General relativity bends the ellipse into a spiral that pulls the grain of sand into the event horizon, where it is lost forever. (I described the reason for this "bending" in the previous article.) Thus the sand does not have to fall directly into the black hole to be captured, it only has to come close. Close will depend on the size of the black hole of course. In our example, you probably need to get within a couple meters. In any case, the grain of sand spirals around and around, approaching the event horizon. Tidal forces shred this miniature rock until it is a swarm of microscopic fragments, then molecules, then atoms. this, and everything else you have dropped into the hole, forms an accretion disk around the event horizon. this is the matter that the black hole is "eating". But a black hole eats like Cookie Monster - it's a messy process. The atoms experience tremendous friction as they whirl around the event horizon. The disk is so hot that it radiates energy in the form of X-rays. Matter is converted into energy at an impressive rate, anywhere from 10 to 30 percent. This is a small black hole, so the conversion is probably less, but anything above 3% is impressive. The best a star can do through nuclear fusion is 0.5%. So if you have some spare mass, you can drop it into a black hole and obtain energy after all. Unfortunately the nature of this energy is rather unpredictable, consisting of X-rays bursting out in all directions at random intervals - and X-rays are difficult to harness for the benefit of a technological civilization. So once again, extracting steady and reliable power from a black hole is difficult, but perhaps not impossible, if you have some disposable mass on-hand.

Further Reading

Electron positron annihilation
Betelgeuse and its apparent magnitude
Black hole and its accretion disk