Escaping a black hole

Factual Questions
21

sturmhauke’s link has the answer (correct or not) to my earlier question. It says “…an outside observer, even one just outside the Schwarzschild surface, can see nothing beyond the horizon.” So does that mean that one’s feet would disappear as he fell into the BH, and his feet crossed the EH?

One answer seems to be that in my example of the two people falling in sequentially, the way time and distance get dilated for them, the second person to be falling in would see the first person getting farther and farther away, without bounds, as that first person approaches the EH. Is this correct? And if you were falling in, would time be stretched so that you never perceive that you actually reach the EH? If true, that sounds like subject matter for a science fiction novel.

22

If you’re falling in, you have a finite (and distressingly short) amount of time, in your reference frame, before you reach the singularity, and you’ll cross the event horizon in an even shorter amount of time. Discussions of “outside observers” usually mean observers who are not falling in; any observer not falling in can’t see anything past the horizon. As you’re falling in, you can always see your feet, but any photons which left your feet from inside the horizon will only reach your eyes after they’re inside the horizon, too. And after you pass the horizon, your feet aren’t pointing “in” any more, since “in” becomes a timelike direction. Instead, your feet would end up pointing along the t direction, which is now a spacelike direction.

23

And it has been the subject for many sf novels and stories. The first, I believe, already has the science exactly right. It’s Poul Anderson’s classic “Kyrie”. Some anthologies it’s been in can be found on this page. An absolute must read.

24

Apparently, exiting a spinning black hole is possible unless one approaches it along the plane of rotation. More strangely, if you approach the singularity at an angle to the plane of rotation, space will become timelike, and then flip back again before your inevitable when becomes a where, you actually feel a repulsive force the closer you get to the singularity (which is a ring, not a point), and are hence deflected to go rocketing off somewhere far away in our universe, or perhaps into another universe. Yow.

Since virtually all natural black holes would be expected to have angular momentum, I guess it would follow that it takes pretty good aim to not escape your average black hole (perhaps even alive?). If the curvature of space outside of the EH isn’t so steep that you’re spaghettified, maybe you fly in, do a little space-time somersault, veer off, and pop out somewhere else completely.

All of this strikes me as…well, more than a little wild, but I must defer to the greater minds of folks like Dr. Roy Kerr and other experts who have worked out the details of the so-called Kerr metric, who tell us this is quite possibly how things actually work.

25

No discussion like this would be complete without the Master’s comments on the subject.

26

You might want to try the BadAstronomy board. They’re very open to questions about this kind of stuff.

27

I see with further reading some rather unequivocal statements to the effect that traversing a spinning black hole, though possible, must never be survivable. Basically, there’s no getting around the fact that as you approach the surface at which your direction of travel becomes time-like again (the so-called Cauchy Horizon), the blue-shift of all matter/energy falling approaches infinity, and you get the mother-of-all-sunburns. Since your direction of travel is space-like after crossing the event-horizon(s?), you’re destined to get fried as surely as tomorrow follows today.

I guess this means “escape” is still potentially possible, but you (as a conscious entity) won’t be around to enjoy it.

Cite.

28

I think you may be confusing two “horizons” of a Kerr-Newman black hole. I pulled my copy of the Phone Book (Misner/Thorne/Wheeler) off the shelf and verified (chapter 33) that there is a “static limit” within which frame-dragging becomes so extreme that no observer can remain at rest with respect to “distant stars”: the Killing vector in the direction of increasing t (the “time” coordinate for distant observers) becomes spacelike within that ellipsoid. The event horizon is a sphere within this ellipsoid, tangent at the poles of rotation. The region inside is the “ergosphere”. Your statements apply to crossing the static limit and entering the ergosphere, but not crossing the event horizon. The statements about being unable to escape the event horizon still apply in full force. Chronos, do I have this right?

29

Hrm. My understanding was that, at the inner edge of the ergosphere, there’s at least one event horizon, and maybe two, depending on if you’re a photon moving in the direction of rotation, or against it. After that, there’s a region where, like a Schwartzchild black hole, space-like and time-like directions are effectively “flipped”, and then you reach the Cauchy Horizon. At the event horizon(s) of a spinning black hole, just as with a Schwartzchild black hole, there’s nothing locally odd about space. But at the Cauchy Horizon, I guess you enter an undefined realm, because the numbers diverge. And then beyond that is the singularity. In that respect, I guess, the Cauchy Horizon acts like another singularity, and some people apparently think it might be highly unstable (for reasons I don’t pretend to grasp). Within the Cauchy Horizon, space and time have one more exchanged places, and you can easily move about the cabin. In fact, it takes infinite effort to approach the singularity unless you do so exactly edge-on. Fly through the ring singularity and you get spat out of an “anti-horizon” into some other realm. Wild.

I gather from my idiot reading of the subject it’s all a big question mark until somebody comes up with workable theory of quantum gravity.

30

I guess I should also add that within the static limit, while it’s impossible to stay still, it’s not impossible to get away; or, at least, so I’ve read. I’m not sure what a “killing vector” is, but if you’re suggesting one is inevitably drawn to the EH in this region, I don’t think that’s true. The static limit is not a horizon, in that sense.

31

A black hole has only one horizon, and it’s strictly one-way. One can theorize a black hole (spinning or not) which would allow escape into another, presumably otherwise unconnected, portion of the Universe, but such a black hole cannot form: If one exists, it must have existed for the entire history of the Universe. There is no evidence for any such hole anywhere in the observable Universe, and if one existed, there probably would be evidence. Any black hole which formed after the beginning must be a deathtrap.

Even in a real black hole, it’s theoretically possible to avoid the singularity, provided that the hole has a charge or rotation. Even there, though, it’s only possible for a point particle which is aimed precisely correctly. For any non-point particle (say, a human), the presense of the particle’s mass would be sufficient to perturb the black hole geometry in such a way that you hit the singularity anyway.

Incidentally, the event horizon of a Kerr (rotating) black hole is not spherical, but it’s less oblate than the boundary of the ergosphere. The boundary of the ergosphere is indeed not a horizon, since one can pass through it and return. In fact, in the ergosphere, one can even steal a little energy from the rotation of the hole, and thereby leave faster than one went in. One just can’t stop while in the ergosphere.

32

Rats!

If you don’t mind, Chronos:

Why do these cites say gravity is repulsive in the vicinity of the singularity of a spinning black hole, unless you approach along the plane of rotation? Is that only true for the point particle you speak of, and things get too disturbed with anything having greater dimension?

33

A Killing vector (capitalized since it’s named after Killing) is – in this situation – a vector such that its Lie derivative applied to the metric is zero. That is, the geometry is invariant under translations in that direction.

As for flipping space and time, that’s basically what I said. Outside the static limit the vector is timelike, but inside it’s spacelike. To stay at the same (r,\phi, heta) coordinates means to move along the t direction, which becomes a spacelike direction inside the static limit.

34

Well, I’m quite certain I didn’t understand much of that, but it’s given me something to read about, at least.

At any rate, what I think you’re saying is there’s a function defining a field that describes motion in a metric such that one can use it to calculate paths that, say, would allow a mass to remain stationary within the static limit. But such a path, effectively, requires traveling faster than light (or following a space-like path). Outside of the static limit, this field would also describe such a path, but it would be time-like. Is this correct? If not, I’ll probably never understand, but I figured I’d bear my ignorance even more for all to see and try to get my head around what you may be saying.

Anyhow, I still don’t think I was mixing up the static limit with horizons in the black hole. I’ve continued reading, and I still come across this idea, in every article that mentions it, that the Kerr metric describes a black hole with two horizons. One of them looks pretty much like the horizon of a Schwartzchild black hole, but inside of that is another one, which is, again, this so-called Cauchy horizon* (non-spinning charged black holes have one of these weird surfaces as well, I guess). Even weirder, the greater the angluar momentum of the hole, the closer together they can get, such that they meet, essentially cancel each other out, and leave the singularity naked. This is physically impossible, so sayeth the experts (involves angular momentum exceeding mass, which, apparently, simply can’t happen), but whatever the nature of this two-horizon picture, it’s not directly related to the static limit.

I guess, from Chronos’s post, whatever these cites are going on about, it’s apparently not a physically realistic picture. I can only infer from what he said that dropping a real mass into a real spinning black hole disturbs this picture such that you don’t encounter or cross this Cauchy horizon, and still wind up following a space-like path all the way into the belly of the beast, to be crushed into the singularity.

*The definition of this horizon is (stolen from wiki): “A light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations). One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics.”

35

I think we should keep in mind that Black Holes are still purely theoretical.

Not every space scientist believes they exist.

36

I’ve never heard that the singularity of a Kerr black hole would be repulsive, but those cites seem to only be discussing so-called maximally extended solutions. These are the theoretical solutions I mentioned above which cannot be formed in the Universe and which must (if they exist) have existed for all time.

The limits on angular momentum and charge of a black hole are based in large part on the fact that super-extreme black holes would have naked singularities, and it’s widely believed that naked singularities are forbidden by nature. There’s also the problem that there’s no known way to evolve a sub-extremal black hole into a super-extreme one. If you try to feed a black hole enough angular momentum or charge to push it past the limit, you’ll also increase its mass, such that the limit creeps away from you.

37

The “Intelligent Design” thread is elsewhere.

38

There is such a thing as a Cauchy horizon, but the fact remains that you can pass through the static limit (which involves “flipping space and time” as you referred to in your first post) and get out, but once you’re through the event horizon you’re in for good.

I won’t say too much abou the Cauchy horizon, but the Cauchy problem in general is to determine sorts of conditions which will allow a given differential equation to be solved uniquely, and to what region that solution can be extended. Two points along a classical particle’s trajectory, for instance, or a point and its velocity at that point will suffice. If you “know the geometry” (in an appropriate sense) of a three-dimensional slice through spacetime at some point in the past you can solve for the four-dimensional geometry of spacetime everywhere outside the Cauchy horizon. This, at least, is what it means to a mathematician.

Now: another pass at Killing vectors. All the standard black hole geometries are “static solutions”, meaning that there is a timelike direction so that moving along that direction is a symmetry of the system. Similarly, they’re axially symmetric, meaning that there’s some axis about which rotations are a symmetry of the system. This is probably easier to get a handle on.

Imagine a sphere with a groove cut along a great circle. Rotating the sphere around the axis perpendicular to that circle is a symmetry – it looks exactly the same before and after. All black hole solutions have such an axis and the angular coordinate is usually called \phi. They also have a coordinate t, and the direction in which t increases is timelike for observers far from the hole. The unit vector in that direction is the Killing vector of the time symmetry. It is also the 4-velocity of a “static” distant observer, and the fact that an observer moving in that direction keeps the same values of r, \phi, and heta is what’s meant by saying the observer “stays in the same place” (relative to the hole).

The situation changes as the observer approaches the static limit: not only does his light-cone tip in towards the hole (as for Schwartzchild geometry), but the rotation of the hole actually drags spacetime itself with it – the light-cone tips in the direction of increasing \phi. The direction of increasing t stays the same, of course. The static limit is the point at which the direction of increasing t becomes spacelike – the light-cone tips until all timelike directions increase \phi. It hasn’t tipped far enough inwards that escape is impossible, though. That happens at the event horizon, which is pretty much how the event horizon is defined.

39

I don’t see what intelligent design has to do with whether black holes exist. Some of the linked pages in this thread suggest that there are some legitimate grievances with black holes; for example one solution leads to an observer falling into a black hole being hit with an infinite amount of energy. I don’t know enough about the subject to argue one way or the other, but apparently some scientists do.

40

Black holes, singularities, whatever you wish to call them, are predicted within General Relativity, and mathematical treatments of various types of holes and their methods of formation are well-developed. While we don’t have any direct observational evidence (in part because black holes are, well, “black” and because there isn’t one in the local neighborhood) we do have a large body of phenomena which correspond with and only with the existance of singularities. I don’t believe that any serious astrophysicist would suggest that they don’t exist, although there is considerable debate over the sizes that could physically come into being (intermediate mass black holes or quantum black holes) and what forms they could take. Some physicsts have suggested that electrons are actually Planck-mass charged singularities, though those claims are entirely speculative.

Stranger