From what I understand, from the point of view of a distant observer, time slows for an object approaching the event horizon of a black hole. The closer the object gets to the event horizon, the more time appears to slow, until it appears to stop altogether as the object reaches the event horizon.

My understanding is that the equations for the apparent time dilation on approaching the event horizon are the same as for time dilation on approaching the speed of light, but I may be wrong on that.

From the point of view of the distant observer, during a finite period of time things may be observed approaching the event horizon, but will never reach it.

But the event horizon is defined as the place where light can no longer escape...so you can never see anything cross the event horizon. And because the intensity of gravity just before you reach that point is actually great enough to stretch out space/time, it stretches the light emitted/reflected from any object going into the black hole out just like stretching out a piece of old fashioned audiotape (assuming that you could stretch audiotape indefinitely without breaking it). The signal attenuates as the observed object approaches the event horizon, but it never breaks.

Time only slows relative to the space traveler/victim of the hole. It wouldn't slow for the observer.

The U.S.S. Unlucky has lost its engines and is travelling toward the event horizon of a black hole.

The Unlucky has a radio beacon on board that sends out a pulse every millisecond, according to the ship's chronometer.

Starbase Observer is receiving that pulse.

Now, by coincidence, the Unlucky is traveling along the straight line between Observer and the event horizon, so we only need to worry about motion in one dimension.

Also, it starts off at a non-relativistic velocity relative to Observer, so initially there is no easily measurable time dilation difference between them.

The Unlucky's current velocity is such that, if there were no acceleration due to gravity and no time dilation, it would reach the event horizon immediately after sending out X pulses on its beacon.

As received by Observer, the interval between each pulse would be slightly longer than one second, because each pulse would come from father away, but that would have nothing to do with time dilation. Observer would receive X pulses in a finite period of time. Let's call that period P1.

But there is acceleration due to gravity. So, if there were no time dilation effects due to either gravity or acceleration, we could easily calculate how fast the Unucky would traverse the distance. Therefore, we could know that its beacon would send Y pulses before it passed the event horizon.

As received by Observer, there would be slightly increasing intervals between each pulse, because the distance traveled by Unlucky between pulses would be increasing, but those increases in the intervals would have nothing to do with time dilation. Observer would receive Y pulses in a finite period of time. Let's call that period P2.

So, now we get to time dilation effects.

Now, from Unlucky's point of view, there is no time dilation of its own chronometer. Therefore, the ship's beacon should send off Y pulses before the ship crosses the event horizon.

From Observer's point of view, if there is time dilation due to gravity slowing the clock on Unlucky as it gets nearer to the event horizon, then the time interval between pulses should keep getting longer. After the period P2 has passed, Observer still will not have received Y pulses. (If it had, then there would not be any time dilation.)

Now, if the time dilation approaches infinity as the Unlucky approaches the event horizon, then the final pulse will be received long after everyone on Station Observer has died and the station's power core has been exhausted.

Since the final pulse from the Unlucky is traveling at the speed of light, no information about what happens to the Unlucky after that pulse can reach Observer before that pulse.

Therefore, the observable size of the black hole cannot have increased due to the addition of the Unlucky.

Since everything falling into a black hole experiences the same type of time dilation as the Unlucky, the observable size of the black hole would take almost an infinite amount of time to increase.

Therefore, a black hole could not get any bigger during the mere billions of years since the Big Bang.

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No, no, no!!!!
Time only slows relative to the space traveler/victim of the hole. It wouldn't slow for the observer.

The force that would suck in space debris is so powerful that it would appear to happen VERY quickly to an outside observer.

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Excellent line of questioning. You're right: as something fall into a blackhole, it appears to approach an infinite redshift. For the Unlucky, it is an entirely different story altogether. They'd be doomed and not know it, and be torn apart by tidal forces long before they even struck the actual blackhole.

You don't actually see the event horizon when you look at a black hole (okay, this is obvious, but you don't directly detect it with any kind of sensor either). You see a sort of infinite tunnel...if you could see the event horizon, it would be at the other end of that infinitely long tunnel...words are failing me here

The problem is that the theoretical geometry and the actual geometry of space near a black hole are two completely different things. To an observer outside the black hole, the event horizon always appears to be an infinite distance away, because...I'm just repeating myself here.

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The really cool postulates I was told about were the ones involving the Not-So-Unlucky, the ship with thrusters strong enough to pull back out of the black hole. Theoretically it would experience time dilation. Theoretically it could even come back out and find that the Universe has all but expired of heat death in the very short (to them) time they've been near the event horizon.

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But here are some more questions:

According to Robin Shelton and J. Allie Cliffe:

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When scientists refer to a spherical cow, we are poking fun at ourselves. We are admitting that some of our models or descriptions of things are far more simple than the actual object, like to say that a cow has a spherical shape. The phenomena we study are often complex, and including too many details can hinder, rather than help our understanding. Often it is useful to study a simplified model which contains only the most important general characteristics. Such a model can be more easily studied using numerical or analytical methods and then compared to observations.

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Kolona,

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Eric, doesn't the acceleration due to gravity always depend on the masses of the objects? That and the distance between them. At least, that's what I've always understood the equation to be saying.

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I believe the distance involved in the calculation is the distance between their centers of mass.

The mass of a black hole is concentrated in the singularity at its center. So the acceleration due to its gravity depends not on the distance from the event horizon, but on the distance from the singularity.

Does the definition of the event horizon mean that the acceleration due to gravity is the same at any event horizon?

r = 2mG/c^2

Now at that location, the acceleration due to gravity would be

a = mG/r^2

= mGc^4/(4m^2G^2)

so that gives

a = c^4 / 4mG

Thus, the acceleration at the Schwarzschild radius would be inversly proportional to the mass of the black hole. The larger the black hole mass, the lower the acceleration. In fact, you could determine the mass necessary to experience one earth normal gravity (g) at the Schwarzschild radius. Set

c^4 / 4mG = g

and solve for m:

m = c^4/4gG

I make it about 5 x 10^17 earth masses or about 1.5 x 10^12 solar masses. Of course, I might easily have made an error ...

Oh, and then the Schwarzschild radius for that blackhole would be 7 x 10^8 earth radii. I think that is about 700 times the radius of the orbit of pluto.

So the thought experiment is just as good as the math for this case.

For the case of the Not-So-Unlucky, if the ship wants to come back out after the universe has passed into oblivion, the crew had better go into a sort of orbit of the black hole rather than trying to go directly in and pull directly back out. There are practical considerations in this, but the main consideration is that if they try just going directly in and then out again, they won't get very much time dilation out of it before they have to turn around and come back out.

You also have to consider that the time dilation effect weakens your actual thrust as measured by an objective observer compared to your percieved thrust...that's a simple matter of practical difficulty again, I'm afraid.

In any case, you can penetrate the event horizon, and in the case of a super-massive black hole, you could even do it safely...well, in that you would survive going through the event horizon, not that you would ever be able to come back out.

Pointing your thrusters at the black hole, you use them to counter the acceleration due to gravity, so you remain where you are 1000km outside the event horizon.

Then, you decrease power to the thrusters slightly, allowing gravity to accelerate you to 1kph. You adjust the thrusters to exactly counter acceleration due to gravity, so you continue moving at 1kph toward the event horizon.

Eventually, you pass through the event horizon. Now you up the thrusters to higher than the acceleration due to gravity. That slows your fall and eventually stops it, at which point you lower the acceleration to exactly counter the pull of gravity.

Now of course, there's all sorts of funky time dilation stuff going as observed by distant observers. But that doesn't matter to you (because hey, you didn't really like the rest of the universe that much anyway.)

Form this situation I want to examine two scenarios.

1. You decide you've had enough fun playing inside a black hole. So you up the acceleration to 2g in order to leave. What prevents you from exiting the event horizon?

To physics, the gravity near the event horizon seems to be one g. An outside observer can't see the event horizon, but can calculate that there will be one g of gravity near it.

...wouldn't this have the effect of creating a graveyard of ghost ships (and other objects), if you will? In other words, wouldn't any object pulled into the black hole seem to be present, frozen at the point where they 'stopped', forever visible there to any outside observer? Is my logic flawed?

Because if that's the case, wouldn't there be a very real way to detect a black hole?

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Theoretically though I think the Science should serve the Story.

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Or anyone else with such info want to share?

But the more interesting technology derivable from zero point energy is an anti-gravity source. See, when you remove energy from empty space, it leaves a kind of hole in the zero-point energy. That hole of below zero energy density acts as (you guessed it) negative mass, which produces (bingo!) negative gravity.

If you generated enough negative gravity, it would be very easy to bust your way out of a black hole. The time dilation wouldn't matter...as the apparent gravity of the black hole seemed to become infinite, the apparent anti-gravitational effect of your negative mass well would also seem to approach infinity.

Of course, you might want to have an infinitely strong ship when this stuff started to go down...but if nothing else got out, your negative mass well still would (of course, without whatever mechanism you used to isolate and maintain it, it would simply meet and cancel out some actual mass energy...if it didn't simply flatten out into the zero-point energy field much like a hole dug in water when you remove whatever is keeping the water out of the hole).

I appreciate the contributions here to the question I hung off Eric's post. I've discovered I need to do a lot of scientific research for a story I'm working on (that's what I get for dropping Physics in high school in favor of Celestial Navigation!). The story isn't about travel in space, but it does have to do with it in a very important way. ZPE had come up of course, and I realized Eric had used it in a post, so thought I would ask. This gets back to my post about recommended reading materials too - I'm working on how my civilization travels in space, and how another group does it too, but not quite in the same way. The basics of FTL travel weren't enough, so I find myself digging into stuff I never had to worry about before - relativity, quantum mechanics, quantum gravity, methods of sublight-speed travel... a lot in search of wormhole info. But, as Kolona said in a post way back, I shouldn't have to do so much I earn a PhD in this stuff... but it seems I do need to know enough to make up a system that people are willing to suspend disbelief for.

On the plus side, I can just sink in and read and take notes, and read and highlight, and draw things, forever on this - no wonder I've loved sf for so long.

On the minus side, I haven't written anything story-like for days (just exercises, notes, and posts).

I'm beginning to understand why people say it takes just as much work to set up a short story as a novel... and I've yet to write a chapter the length of a, well, chapter!

Maybe I'll create the Chiu-Dalton Portal!