So you've decided to spend your vacation falling into a black hole, just to see what it's like? Good choice. Here are the highlights of what to expect:

First, you must locate a black hole. There is certainly a black hole at the center of our galaxy, but you don't have enough vacation time saved up to get there. So, look in the local vicinity for places of high X-ray emission. No, the local clinic just won't do.

The next step is getting to the black hole. Assuming you can afford a spaceship, the nearest ones are tens to hundreds of light-years away, but you can save time by accelerating yourself to relativistic speeds and taking advantage of time dilation. It does eat up the fuel budget a bit. though.

Once you've arrived, you can start falling in. The first thing you will notice is other matter falling in with you. Although there may be black holes without matter falling into them already, you won't have detected them because the X-rays we mentioned are emitted from the infalling matter before it passes the point of no return.

If your black hole is spinning, the matter will have formed into an accretion disk around the black hole's equator (it has one because it's spinning). If it's not spinning, it will be falling in from everywhere. This will be inconvenient since you don't want it to touch your spaceship: It's probably at a temperature of several million degrees.

Now's where the fun begins. Assuming you avoided the other infalling matter, as you get closer, you will begin to feel like your head is pulling away from your feet. This is due to tidal forces: The black hole has a strong gravity field, but this field grows much stronger the closer you get. Assuming you're falling in feet first, the hole is pulling harder on your feet than on your head. You must switch on your antigravity1 in order to keep you and your spaceship from being pulled into a big piece of metal spaghetti with a bit of nasty liquid somewhere inside.

Another thing you will notice is that the radio broadcasts have slowed down. You will think you're listening to Camille Saint-Saens' turtles when you're really listening to Jacques Offenbach's Orpheus in the Underworld2. This is time dilation again; only instead of saving you time, it's costing you time. You have a chance of turning around and going home, but you had still better call your boss.

As you get closer still, you will notice the black hole. Well, you'll certainly notice a big nothing, where there aren't any stars or blinding white light from the accretion disk.

You will also notice that the hole appears to be growing alarmingly fast, much faster than you might expect from simply getting closer to it. This is the black hole's gravity field again; it's so strong that it bends the light that manages to escape. This bending of light makes the hole appear to take up much more of your field of vision than it really does.

Eventually you will reach a point, 1.5 Schwarzchild radii from the hole, where the black hole appears to take up half the sky: An unbroken black wall that stretches to infinity in all directions3. As you get closer still, the rest of the Universe appears to take up increasingly small parts of the sky.

Eventually, the Universe shrinks to a blinding white pinpoint behind you. This may put a hole in your spaceship as it is all of the radiation emitted by the Universe until its heat death4. Oh, I forgot to tell you, due to time dilation the entire remainder of the History of the Universe has passed while you were malingering round this thing. I expect your job will have been filled.

At some point you will cross the event horizon of the black hole.  If it's a spinning black hole you may (according to one theory) be spat out of a white hole5 into a brand new Universe.  But as we've discovered, there's no going back.

1I hope you remembered to have antigravity installed.
2Saint-Saens' piece was a parody of Offenbach's piece,a can-can dance slowed down to a crawl.
3The other infalling matter will provide illumination, falling beside you in a kind of endless vertical meteor shower.
4At which point, the pinpoint of light will go out.
5I don't much go for this white hole nonsense; time dilation being what it is, I expect all of the infalling matter will have been reduced to primordial quantum soup and emitted into the new Universe at the same time.  All of it at the same time.  Sounds like what they call a Big Bang to me.

Also, so interesting effects would be seen by an observer who stayed behind (a safe distance from the Black Hole). First of all, the observer would never actually see you cross the event horizon. This is because of time dilation. You would appear to be gettng closer and closer, but never actually cross the event horizon. It would also be very hard to see you anyway as the light reflecting off you would have a hard time getting away from the gravitational pull of the hole. As you got closer, light would leave the area with longer and longer wavelengths because of gravitational red shift. This would make you very difficult to see as the light shifted out of the visible spectrum.

There's a lot of speculation and science fiction devoted to the idea of what may happen when a person falls into a black hole. I don't know all the physics of a rotating black hole, but it is impossible to fall into a nonrotating one (even if the person were to survive the radiation and tidal effects, and other hazards mentioned by Gorgonzola). The reason is quite simple: It takes a (theoretically) infinite amount of time, as measured by an 'external' observer, for any object to reach the event horizon (as mentioned by viper281). However - black holes do not exist for an infinite amount of time. Hawking radiation causes them to evaporate.

As viewed from outside, a person falling towards a nonrotating black hole will appear to slow down. The watch on the faller's wrist will appear to tick slower and slower. The faller will never touch the event horizon, and if the observer keeps watching on long enough time frames, the hole will shrink. What happens when the event horizon radius reaches zero, I don't know (some claim a naked singularity).

As viewed by the faller, the watch on the external viewer's wrist will appear to tick faster and faster as the event horizon approaches. The same Hawking radiation that the external observer sees, the faller will also see, only at a much much faster rate because of gravitational time dilation. The time dilation will always work to shrink the black hole to nothing before the faller has 'time' to hit it.

This idea has an important consequence in considering the formation of (nonrotating) black holes: that is, they never fully form at all! The outermost layer of a collapsing star will fall towards the event horizon - but will never get there. There will never be a black hole in which all the mass is within the event horizon radius, because the mass has to fall in from someplace outside of that radius, and anything outside never finishes falling in. One might make quantum theory arguments about how all the mass can get inside the event horizon, but to the best of my knowledge, current quantum theory is not applicable at the limits of gravitational effects. In other words, where BlakJak says "The occurence of black holes is a result of a star's state of collapse causing it to be smaller than its own Schwarzschild radius", the time dilation experienced by the outer shell combined with the Hawking radiation actually prevents that state from ever really happening.

One more thing worth noting: Every massive object has a Schwartzschild radius. An electron has a Schwartzschild radius. The Earth has a Schwartzschild radius. However, the radius of the Earth is greater than it's Schwartzschild radius, which is why we're not living on/in a black hole.

I just realised, I'm not sure if the black hole I describe in my writeup needs to be electrically neutral too. A charged black hole may have extra properties which cause even further complications. For the sake of simplicity, pretend I've been writing about a neutral black hole all along.

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