Does the Black Hole Myth Hold True?

[Khashishi]

I came across this website which basically contradicts most of what I've heard about a black hole.
http://www.engr.newpaltz.edu/~biswast/bhole/blackhole.shtml

In particular, it claims that it's possible to escape a black hole by reversing one's momentum after crossing the event horizon.

Is that right? It seems reasonable if we treat mechanics as time-reversible; yet, almost everyone says that nothing can escape a black hole. If nothing can escape a black hole, what is the time reverse of an object free-falling into a black hole?

 

[PeterDonis]

In particular, it claims that it's possible to escape a black hole by reversing one's momentum after crossing the event horizon.

Is that right?

No. Once you are inside the horizon, you are going to hit the singularity at the center of the hole no matter what you do. Reversing your momentum will somewhat extend the time it takes you to hit the singularity, but it won't stop you from doing so.

It seems reasonable if we treat mechanics as time-reversible; yet, almost everyone says that nothing can escape a black hole. If nothing can escape a black hole, what is the time reverse of an object free-falling into a black hole?

The short answer is, an object rising up out of a white hole. However, there are a *lot* of complications lurking underneath.

On a quick skim of the web page you linked to, it looks like the author has some confusions and misconceptions about the physics of black holes, and about how black holes can form from the gravitational collapse of objects like stars.

 

[Goodison_Lad]

The simple answer is no, it is not possible to escape from a black hole once you've crossed the event horizon.

The link you gave gives a mixture of accurate science and confused assertions. To 'time reverse' seems to me to be no more than filming it then running the film backwards then saying that you can escape. I can fall down an ordinary well. Running the film of my misfortune backwards won't get me out of the well. Saying that the ship could escape from inside a black hole 'if somehow one could reverse its momentum' might seem plausible, except that the force required would be infinite.

An object starting at great distance and falling into a black hole crosses the event horizon at the speed of light. The escape velocity (i.e. the velocity required to stay permanently outside the black hole) is equal to the speed of light at the black hole's 'surface' (the event horizon). Since a spaceship can't even attain the speed of light, let alone exceed it, I'm afraid you'd be stuck inside the event horizon, and very soon end up at the singularity at the centre.

 

[PAllen]

I find the arguments on the link unpersuasive. In particular, the argument about reversing momentum ignores the geometry of the region:

Yes, if you have gone from event B to event A you can always reverse the direction of your momentum at A. The claim that this will take you back to event B is absurd - it is in your past. The claim that it will take you back to the spatial location of B requires that the geometry is static - false for the complete SC geometry. (myth #4 argument)

The arguments on impossibility of forming a black hole (myth #2) don't even mention the singularity theorems, so they cannot be taken seriously at all.


For reference, here are the two papers on this I could find on arxiv by this author. Neither has been published (nor is there even a mention of submittal for peer review):

http://arxiv.org/abs/0809.1452
http://arxiv.org/abs/1006.4185

(The author is an associate professor of physics at SUNY New Paltz, community college, thus not without some credentials).

 

[PeterDonis]

For reference, here are the two papers on this I could find on arxiv by this author. Neither has been published (nor is there even a mention of submittal for peer review):

http://arxiv.org/abs/0809.1452
http://arxiv.org/abs/1006.4185

(The author is an associate professor of physics at SUNY New Paltz, community college, thus not without some credentials).

Very interesting. Some of what he says could be interpreted (charitably) as taking a very unconventional but still possibly defensible viewpoint. However, it's hard to tell if he really intends that, or if he is just confused.

 

[Khashishi]

Thanks. I've been staring at a Kruskal-Szekeres coordinate plot, and it sort of makes sense, although it seems to imply that every black hole is also a white hole in the past of a falling object. Where is this white hole located in the asymptotic observer's coordinates?

Reversing one's momentum only makes sense with respect to a local observer. I don't suppose there's any way to define a momentum inside the black hole relative to an observer outside the black hole.

 

[elfmotat]

Reversing your momentum will somewhat extend the time it takes you to hit the singularity, but it won't stop you from doing so.

If I'm not mistaken, it actually won't (according to his clock anyway). Isn't the path of maximum proper time a free-fall path?

 

[PAllen]

If I'm not mistaken, it actually won't (according to his clock anyway). Isn't the path of maximum proper time a free-fall path?

This is a bit tricky. Free fall gives maximum proper time between two nearby events (not more than that, in GR, in general). The singularity is not an event. The most, I think, you can say is that for any event inside the event horizon, there exists a free fall geodesic that has maximal proper time among all paths from that event to the singularity. There will be many(all) other free fall paths (as well as non-free fall) that reach the singularity in less proper time. If you happen to be on this free fall geodesic any change in motion you make will shorten your time to the singularity. However, if you are on any other free fall geodesic through the given event, you can lengthen the time to reach the singularity by changing your motion.

 

[PeterDonis]

Thanks. I've been staring at a Kruskal-Szekeres coordinate plot, and it sort of makes sense, although it seems to imply that every black hole is also a white hole in the past of a falling object. Where is this white hole located in the asymptotic observer's coordinates?

To the past of t = minus infinity (just as the black hole is to the future of t = plus infinity).

 

[m4r35n357]

The author provides a link to download his program: http://www.engr.newpaltz.edu/~biswast/bhole/orbit.shtml
Unfortunately it is a Windows program so I can't run it, and it's an executable so I can't build it, but it might just be possible to check its output against GROrbits.

 

[Demystifier]

In particular, it claims that it's possible to escape a black hole by reversing one's momentum after crossing the event horizon.

Is that right? It seems reasonable if we treat mechanics as time-reversible; yet, almost everyone says that nothing can escape a black hole. If nothing can escape a black hole, what is the time reverse of an object free-falling into a black hole?

One should distinguish 3-momentum from 4-momentum. By reversing 3-momentum, you cannot escape from black hole. If you could inverse the 4-momentum, including the time-component of it, it would mean that your energy would reverse the sign, which would be equivalent to reverse the direction of time. If you could do that, you could escape from the black hole. But of course, in reality you cannot reverse the sign of energy and the direction of time.

 

[Ich]

If you could inverse the 4-momentum, including the time-component of it, it would mean that your energy would reverse the sign, which would be equivalent to reverse the direction of time.

Exactly. The author obviously mistakenly assumes that $m\partial r/ \partial \tau$ is spacelike momentum, and that one could revert it with a finite amount of energy. But inside the horizon, the Schwarzschlild r-coordinate is timelike. He could change $\partial t/ \partial \tau$, though, but it wouldn't help him escape.

 

[DrewD]

The scary thing is that the author has a Ph.D and appears to be one of two associate professors at SUNY New Paltz! There's nothing wrong with disagreeing with the status quo, but he doesn't seem to make very coherent arguments.

 

[Demystifier]

Few additional comments on time-reversal invariance of black holes.

The maximal analytic extension of Schwarzschild metric is Kruskal spacetime which contains both black and white hole. From the white hole you can escape out (but not fall in), which is the the time-reversal of the black hole. Thus, it is fully time-reversal invariant.

However, such a solution describes an eternal "black-and-white" hole, not a real black hole created through a gravitational collapse. The mere fact that an object is created through a collapse breaks the time-inversion invariance, so one should not be surprised that a real black hole is not time-inversion invariant. For systems with attractive force (such as gravity) it can be shown that collapse increases entropy, so the natural time-direction is the one in which matter collapses, rather than de-collapses. Escaping from the black hole would be against the second law of thermodynamics. In fact, it would be traveling to the past.

 

[Sam Gralla]

Haha that's pretty funny. He doesn't actually make an argument, but I think he's actually just using the uniqueness theorem for ordinary differential equations, together with the assumption that you can move backwards in time. Needless to say, this assumption is at odds with experiment =). Very funny.