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# Black holes

So gravity pulls on light just as on rocks. We also know that we can put rocks in orbit, can we put light in orbit? Yes! but we need a very heavy object whose radius is very small, for example, we need something as heavy as the sun but squashed to a radius of less than about 3km. Given such an object, light moving towards it in the right direction will, if it comes close enough land in an orbit around it. If you place yourself in the path of light as it orbits the object, you'd be able to see your back.

But we can go farther and imagine an object so massive and compact that if we turn on a laser beam on its surface gravity's pull will bend it back towards the surface. Think what this means: since no light can leave this object it will appear perfectly black, this is a black hole. An object which comes sufficiently close to a black hole will also disappear into it (since nothing moves faster than light if an object traps light it will also trap everything else).

The effect of a black holes, like all gravitational effects, decreases with distance. This means that there will be a boundary'' surrounding the black hole such that anything crossing it will be unable to leave the region near the black hole; this boundary is called the black-hole horizon see Fig. 7.10 Anything crossing the horizon is permanently trapped. Black holes are prefect roach motels: once you check in (by crossing the horizon), you never check out.

The distance from the black hole to the horizon is determined by the mass of the black hole: the larger the mass the mode distant is the horizon from the center. For a black hole with the same mass as out sun the horizon is about 3 km from the center; for black holes with a billion solar masses (yes there are such things) this is increased to 3×109 km, about the distance from the sun to Uranus. For very massive black holes the horizon is so far away from the center that an observer crossing it might not realize what has just happened, only later, when all efforts to leave the area prove futile, the dreadful realization of what happened will set in.

Imagine a brave (dumb?) astronaut who decides to through the horizon and into the nearest black hole and let us follow his observations. The first effects that becomes noticeable as he approaches the event horizon is that his clock ticks slower and slower with respect to the clocks on his spaceship very far from the black hole (see Sect. 7.4) to the point that it will take infinite spaceship time for him to cross the horizon. In contrast it will take a finite amount of astronaut time to cross the horizon, an extreme case of the relativity of time.

As the astronaut approaches the horizon the light he emits will be more and more shifted towards the red (see Sect. 7.4) eventually reaching the infrared, then microwaves, then radio, etc. In order to see him the spaceship will eventually have to detect first infrared light, then radio waves, then microwaves, etc.

After crossing the horizon the astronaut stays inside. Even though the crossing of the horizon might not be a traumatic experience the same cannot be said for his ultimate fate. Suppose he decides to fall feet first, then, when sufficiently close to the black hole, the gravitational pull on his feet will be much larger than that on his head and he will be literally ripped to pieces.

So far black holes appear an unfalsifiable conclusion of the General Theory of Relativity: their properties are such that no radiation comes out of them so they cannot be detected from a distance, and if you should decide to go, you cannot come back to tell your pals whether it really was a black hole or whether you died in a freak accident. Doesn't this contradict the basic requirement that a scientific theory be falsifiable (Sect. 1.2.1)?

Well, no, General Theory of Relativity even in this one of its most extreme predictions is falsifiable. The saving circumstance is provided by the matter surrounding the black hole. All such stuff is continuously being dragged into the hole (see Fig. 7.11) and devoured, but in the process it gets extremely hot and radiates light, ultraviolet radiation and X rays. Moreover, this cosmic Maelstrom is so chaotic that the radiation changes very rapidly, sometimes very intense, sometimes much weaker, and these changes come very rapidly (see Fig. 7.12). From this changes one can estimate the size of the object generating the radiation.

On the other hand astronomers can see the gravitational effects on near-by stars of whatever is making the radiation. And from these effects they can estimate the mass of the beast. Knowing then the size, the manner in which matter radiates when it comes near, and the mass one can compare this to the predictions of General Theory of Relativity and decide whether this is a black hole or not. The best candidate for a black hole found in this way is called Cygnus X1 (the first observed X ray source in the constellation Cygnus, the swan).

All the ways we have of detecting black holes depend on the manner in which they affect the matter surrounding them. The most striking example is provided by some observation of very distant X-ray sources which are known to be relatively compact (galaxy size) and very far away. Then the very fact that we can see them implies that they are extremely bright objects, so bright that we know of only one source that can fuel them: the radiation given off by matter while being swallowed by a black hole . So the picture we have of these objects, generically called active galactic nuclei, is that of a supermassive (a billion solar masses or so) black hole assimilating many stars per second, and in disappearing these stars give off the energy that announces their demise.

All this from the (apparently) innocent principle of equivalence.

Next: Gravitation and energy Up: The General Theory of Previous: Clocks in a gravitational
Jose Wudka
9/24/1998