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3166 clicks; posted to Geek » on 04 Oct 2012 at 12:05 PM (4 years ago)   |   Favorite    |   share:    more»

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Myria: Theaetetus: Myria: Why can't you escape from a black hole by firing a rocket straight down continuously? Escape speed is only meaningful when gravity is the only force, right?

I kind of suck at physics, so I probably don't understand something fundamental here.

Y'know how the Earth is pretty big and gravity pulls you to it? One jump isn't going to do it. To leave, you need to get up to 11.2 km/s (25,000 mph).
That's a lot, but consider Jupiter. A huge honking planet. You need to be going 59.5 km/s to leave there.
And if you were on the surface of the sun (ouch), you need to be going 617.5km/s.
And a black hole? Well, at its event horizon, you need to get up to 299,792.458 km/s. And you can't build a rocket that can propel you that fast, because it would take an infinite amount of energy.

But doesn't the concept of escape speed not apply if you have propulsion the whole time? See "Misconception" in Wikipedia's article on escape speed/velocity.

True, provided you have enough propulsion to overcome the gravitational force pulling you in. So, for example, if you had a rocket that could accelerate you at 10m/s^2*, you'd eventually lift off from Earth and escape.
With a black hole, it gets a little more difficult... The radius of the event horizon of an ordinary black hole is R = 2GM/c^2, and so the gravitational acceleration at that radius is c^4/4GM. So, for example, given a black hole with a mass of 10 Sols, you get an acceleration of 3.80351459 × 10^12 m / s^2. If you can beat that continuously, you can get away... Inside the event horizon, however, the relativistic effects change things around. Space becomes timelike, and as a result, it's not actually possible to escape, even with an infinite acceleration.

*the requirement would reduce slightly as you got farther away

Theaetetus: Inside the event horizon, however, the relativistic effects change things around. Space becomes timelike, and as a result, it's not actually possible to escape, even with an infinite acceleration.

Space doesn't become timelike. The Schwarzschild radial coordinate, which is spacelike outside the horizon, becomes timelike inside the horizon. But there are other (arguably, better) coordinate systems in which this does not happen, and anyway, anything that is a coordinate artifact can't influence coordinate-independent events such as an observer escaping a black hole.

What is true is that inside the horizon, all timelike worldlines intersect the singularity, and none intersect the horizon.

Ambitwistor: Theaetetus: Inside the event horizon, however, the relativistic effects change things around. Space becomes timelike, and as a result, it's not actually possible to escape, even with an infinite acceleration.

Space doesn't become timelike. The Schwarzschild radial coordinate, which is spacelike outside the horizon, becomes timelike inside the horizon. But there are other (arguably, better) coordinate systems in which this does not happen, and anyway, anything that is a coordinate artifact can't influence coordinate-independent events such as an observer escaping a black hole.

What is true is that inside the horizon, all timelike worldlines intersect the singularity, and none intersect the horizon.

Fair enough. I respectfully defer to the learned astrophysicist.

Below is a Kruskal diagram of what's going on. The horizon is the 45-degree cone structure, and the singularity is the jagged hyperbola.

The important thing to note is that anybody traveling slower than light follows a trajectory that makes an angle with the vertical of less than 45 degrees (such as the example depicted of an infalling object). You can see geometrically that all such trajectories end up hitting the singularity, and that once you're within the horizon (inside the top triangular region), you'd need to travel at an angle of greater than 45 degrees (i.e., faster than light) to escape (pass outside the triangle before hitting the singularity).

Ambitwistor: Myria: But doesn't the concept of escape speed not apply if you have propulsion the whole time? See "Misconception" in Wikipedia's article on escape speed/velocity.

Yes. This is why escape from a black hole is different from "escape velocity" in Newtonian gravity. You could escape a "Newtonian black hole" (an object whose surface gravity is great enough that its escape velocity is greater than the speed of light) by accelerating hard enough. But you can't escape an Einsteinian black hole with any acceleration, because spacetime curves inward upon itself to deflect all trajectories toward the interior singularity. The only way to escape an Einsteinian black hole is to go faster than light, but in relativity there's no acceleration or amount of energy that will let you do that.

Expanding on the idea....

Once you're inside the Event Horizon, every possible path you can physically take in spacetime leads toward the singularity at the heart of the black hole. Spacetime within the EH is bent 100% toward it. In fact, the faster you move if you try to escape, the faster you accelerate toward the singularity. It's irrevocably in your future.

Put more simply: Inside the Event Horizon, there is no direction you can physically point your spaceship where the singularity isn't in front of you.

BKITU: In fact, the faster you move if you try to escape, the faster you accelerate toward the singularity.

Good point, and kind of counter-intuitive. If you want to survive as long as possible, do nothing: just fall. Any attempt of yours to accelerate, in any direction, will make you hit the singularity faster according to your clock, due to the time dilation of your motion. (Geodesics are worldlines of extremal proper time.)

Put more simply: Inside the Event Horizon, there is no direction you can physically point your spaceship where the singularity isn't in front of you.

Well, you can face away from the singularity (e.g., to see outside the hole), but it is always in your future.

Yeah but if you mess with it in flight you never come back.

Does anyone know if you could escape the event horizon of a black hole with an Alcubierre drive or some other means of FTL travel? If you could then you could zoom in, view the singularity, then leave.

flaminio: Go on. I'm listening...

Q: How do you escape from a black hole.

A: Very slowly.

Sometimes you gotta fly into the black hole to make sure you kill Chiggy von Richthofen.

Loving all these sci-fi references...

I was going to comment that a warp core ejection is only used to seal a subspace tear, never a blackhole, then I remembered my JJ Abramology...

Aborted Baby Jesus Fetus: Does anyone know if you could escape the event horizon of a black hole with an Alcubierre drive or some other means of FTL travel? If you could then you could zoom in, view the singularity, then leave.

It would probably be a pain to work out the math, but my guess is that an Alcubierre warp drive could escape an event horizon. However, as born_yesterday noted, this would require the existence of exotic matter that doesn't appear to exist (and would cause all kinds of causality/time travel problems if it did).

Ambitwistor: Well, you can face away from the singularity (e.g., to see outside the hole), but it is always in your future.

Well, technically you have no choice when it comes to facing away from the singularity. Seeing the singulairy itself would require information to be carried along a spacelike worldline. :-)

Just for fun though, Myria, I'll throw a wrench in the works. There IS one way to classically (read: non-FTL) escape the event horizon of a black hole, but it still falls into the "this-shiat-will-NEVER-happen-without-divine-intervention" category.

Long story short, in addition to mass and angular momentum terms, there's also a term for electric charge in the equations for the calculation of a black hole's event horizon. Black holes are, by statistical necessity, effectively electrically neutral. But that charge term is always present; and if it's not set to zero, your event horizon can shrink. Hypothetically, VERY hypothetically, a rocket that has fallen into the event horizon of a black hole could asymmetrically dischage a few quadrillion terafarad capacitors such that the singularity aquires a sufficient charge; and for the briefest of moments of time, cause the event horizon to shrink such that the rocket is once again outside. A large enough charge could (hypothetically) cause the event horizon to disappear completely; yielding a structure that has been named a "naked" singularity. However, this also leaves the singularity as a VERY attractive target for particles of the opposite charge, and shortly thereafter, the singularity will neutralize it's charge and the event horizon will reform. If the rocket wants to escape, it needs to act very quickly.

The capacitor discharge would be the equivalent of your freshman gym class where the senior ran up behind you and pantsed you. Naturally, you would pull you pants back up very quickly to stop the escape of spacelike information about your genitals. But for those brief, hilarious moments, the rocket is once again visible to the outside world. Singularities don't want to be naked.

Flt209er: Well, technically you have no choice when it comes to facing away from the singularity. Seeing the singulairy itself would require information to be carried along a spacelike worldline. :-)

It's possible to face either toward or away from the singularity. You just can't see it. (Just like you can face toward a horizon, but can't see inside it.)

There IS one way to classically (read: non-FTL) escape the event horizon of a black hole, but it still falls into the "this-shiat-will-NEVER-happen-without-divine-intervention" category. [...] However, this also leaves the singularity as a VERY attractive target for particles of the opposite charge, and shortly thereafter, the singularity will neutralize it's charge and the event horizon will reform.

IMHO, it's likely that if you could calculate quantum field backreactions on the naked singularity (which you can't do without quantum gravity), you'd find there isn't one ...

Ambitwistor: IMHO, it's likely that if you could calculate quantum field backreactions on the naked singularity (which you can't do without quantum gravity), you'd find there isn't one ...

You'd find that there isn't a backreaction? A singularity? I'm an E&M guy by day; I'd be tempted to just treat the thing like an oversized (undersized?) electron, but I'm not well versed at all in the QG theories. I'm curious what you're expecting to not find; if you'd care to elaborate a bit.

And fine, you could face the singularity. I'd just be a really boring view.

Flt209er: Ambitwistor: IMHO, it's likely that if you could calculate quantum field backreactions on the naked singularity (which you can't do without quantum gravity), you'd find there isn't one ...

You'd find that there isn't a backreaction? A singularity?

A naked singularity.

I'm an E&M guy by day; I'd be tempted to just treat the thing like an oversized (undersized?) electron, but I'm not well versed at all in the QG theories.

You can't really treat it at all; it's literally a "hole" in spacetime so you can't define how a field interacts with it. You can compute the effects of curved spacetime on quantum fields, and to a limited extent compute low-order backreaction corrections of quantum fields back onto spacetime, but this fails utterly when applied to a spacetime singularity. String theory might have an approximate way to compute this, but I'm not well versed on what string theory has to say about naked singularities.

Ambitwistor: A naked singularity...this fails utterly when applied to a spacetime singularity.

Gotcha. And for the record, I agree.

But that's exactly why I'd be tempted to treat it like an electron. It was relatively clear pretty early on that the electron couldn't be considered a point charge because the math just didn't work. Don't worry, I'm well aware of how many failed approaches are out there, and I hold no illusions that the answer is as simplistic as just "treating it like an electron." But along the same lines, I'd bet a significant amount of money that there's never just a "hole" in spacetime regardless of singularity type. Maybe that singularity can be smeared over four or five dimensions, maybe it needs 11. But a literal discontinuity (at non-zero energies)? Eh, doubtful.

Flt209er: But that's exactly why I'd be tempted to treat it like an electron. It was relatively clear pretty early on that the electron couldn't be considered a point charge because the math just didn't work. Don't worry, I'm well aware of how many failed approaches are out there, and I hold no illusions that the answer is as simplistic as just "treating it like an electron."

The problem is can't give a singularity properties like charge or spin because it is, quite literally, a hole in the spacetime manifold where no mathematical properties exist.

But along the same lines, I'd bet a significant amount of money that there's never just a "hole" in spacetime regardless of singularity type. Maybe that singularity can be smeared over four or five dimensions, maybe it needs 11. But a literal discontinuity (at non-zero energies)? Eh, doubtful.

I think most people on quantum gravity suspect that true singularities don't really exist; they're either "smeared out", or spacetime is discrete and there is just some Planck-scale geometric feature there, or whatever.

Ambitwistor: KarmicDisaster: The problem is going to be that since it took an infinite amount of time for you to fall into the black hole (from the outside universe point of view) in the first place that everything will be over once you escape.

It just appears to take an infinite amount of time. If you look at what's going on in a causal spacetime diagram (e.g., Kruskal-Szekeres coordinates), you could in principle enter the black hole and escape it again in finite time according to an outside observer, if you could travel faster than light. The problem, of course, is you can't travel FTL, and therefore can't escape in the first place.

Well, yeah.

Does anyone else remember when Time wrote for adults? Or hired them to write?

Ambitwistor: Theaetetus: Inside the event horizon, however, the relativistic effects change things around. Space becomes timelike, and as a result, it's not actually possible to escape, even with an infinite acceleration.

Space doesn't become timelike. The Schwarzschild radial coordinate, which is spacelike outside the horizon, becomes timelike inside the horizon. But there are other (arguably, better) coordinate systems in which this does not happen, and anyway, anything that is a coordinate artifact can't influence coordinate-independent events such as an observer escaping a black hole.

What is true is that inside the horizon, all timelike worldlines intersect the singularity, and none intersect the horizon.

What about a sufficiently large toroid rotating black hole? If the event horizons in the center of the body overlapped, wouldn't it be possible to cross the horizon's border and "shoot the hoop", so to speak?

Oh, never mind. Answered my own question. The interior metric of that solution (toroid) is extremely unstable, so you'd probably never get the chance.

Divorce.

You surf the luck plane and get the F outta there!

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