Contractions with black holes

[retina]

Theories about black holes offten state some simple rules:

<1> - the material inside shrinks to a singularity.
<2> - nothing can escape the event horizon once it gets inside.
<3> - naturally formed black holes will most likely have spin.
<4> - any spin creates a "gravational wash" that drags things around.

It seems that <2> (info escaping) and <4> ("wash") are mutually exclusive. Since the spin can be measured by the extent of the "wash" force generated then information about the spin must escaping from the hole. All the reports and books I have read never say anything about this.

As a follow on from that, and assuming that the wash is real then it seems that <1> (shrinking) would eventually create an infinite spin (think of a ballet dancer spinning and drawing in her arms) and thus an infinite draging force but this has never been observed. If the amount of drag force was infinite it would preclude anything actually falling in, and probably fling back anything that approaches. Also, being infinite, the force would actually extend far beyond the event horizon to everywhere. But since we are all here to talk about it then this clearly does not happen.

Has black hole theory gone awry, or is there some peculiar force/event/rule/thing that governs this situation?

[xilman]

Originally Posted by retina

Theories about black holes offten state some simple rules:

<1> - the material inside shrinks to a singularity.
<2> - nothing can escape the event horizon once it gets inside.
<3> - naturally formed black holes will most likely have spin.
<4> - any spin creates a "gravational wash" that drags things around.

It seems that <2> (info escaping) and <4> ("wash") are mutually exclusive. Since the spin can be measured by the extent of the "wash" force generated then information about the spin must escaping from the hole. All the reports and books I have read never say anything about this.

As a follow on from that, and assuming that the wash is real then it seems that <1> (shrinking) would eventually create an infinite spin (think of a ballet dancer spinning and drawing in her arms) and thus an infinite draging force but this has never been observed. If the amount of drag force was infinite it would preclude anything actually falling in, and probably fling back anything that approaches. Also, being infinite, the force would actually extend far beyond the event horizon to everywhere. But since we are all here to talk about it then this clearly does not happen.

Has black hole theory gone awry, or is there some peculiar force/event/rule/thing that governs this situation?

For a start, you may wish to read some better books on general relativity as the one's you've found so far are clearly inadequate. I still regard "Gravitation" by Misner, Thorne & Wheeler as the best one around. However, it's moderately expensive and assumes at least 1st year undergraduate physics.

There is no conflict between your [2] and [4]. The critical point is that the "wash" as you call it (the standard term is "frame dragging") occurs outside the event horizon and nothing is escaping from inside the hole. The celebrated "no-hair" theorem says that the only properties of a BH that are measurable externally are the mass (put things near to the BH and observe their paths), the angular momentum (measure frame dragging near the BH) and electrical charge (put charged bodies near the BH and observe their paths). Everything else gets smoothed out (by the emission of radiation) shortly after the BH is created.

Nothing inside the event horizon of a classical (i.e non-quantum) BH is observable from outside, so your concerns about infinite frame dragging are exactly on a par with infinite density, infinite spacetime curvature (aka gravitational fields) and so forth.

Any massive object will cause frame dragging according to GR. You may find the search term LAGEOS illuminating.

Paul

[retina]

... "frame dragging") occurs outside the event horizon and nothing is escaping from inside the hole.

If I throw in a large solar system or two and wait a while while they nestle down into the singularity, will I see (feel) the frame dragging increase/decrease (after adjusting our calculations for the change in mass), if I do see this then are we not measuring the effect of events inside the BH and thus information about the change in spin? If I toss in a large planet at 0.99...9c at a trajectory against the spin I should expect to measure a decrease in the spin. Chuck in a few more planets like that and perhaps I can get it to reverse it's spin?

[xilman]

Originally Posted by retina

If I throw in a large solar system or two and wait a while while they nestle down into the singularity, will I see (feel) the frame dragging increase/decrease (after adjusting our calculations for the change in mass), if I do see this then are we not measuring the effect of events inside the BH and thus information about the change in spin? If I toss in a large planet at 0.99...9c at a trajectory against the spin I should expect to measure a decrease in the spin. Chuck in a few more planets like that and perhaps I can get it to reverse it's spin?

You can certainly change the angular momentum of a BH, in exactly the same way that you can change the mass and the electric charge. You do this by throwing in material with angular momentum, exactly as you change the mass by throwing in mass and change the charge by throwing in electrically charged material. Throw in enough angular momentum opposed to that of the BH and, yes, you can indeed get it to reverse its spin. One way is to throw it in non-radially in an orbit (necessarily a decaying one) which is retrograde with respect to the BH. Incidentally, this is an *extremely* efficient way of extracting energy from the combined system of BH + infalling matter.

You are not measuring the effects of things happening inside the singularity or even inside the event horizon. What you're measuring is the angular momentum of a region of spacetime which happens, initially, to contain a black hole together with an infalling solar system and, finally, only a black hole. The two measurements will be equal because angular momentum is conserved.

Paul

[ewmayer]

A more interesting issue which I'll leave as an exercise for the motivated reader is: does Hawking radiation violate the second law of thermodynamics? We know from the by-now well-established theory of black hole thermodynamics (BHT) that the entropy of a black hole is proportional to the area of its event horizon, hence the more massive the black hole, the greater its entropy. On the other hand, BHT also predicts that an isolated black hole (i.e. one with no external influx of mass/energy) will slowly lose mass and "evaporate" (though on a typical timescale tremendously larger than that of the present age of the known universe) via Hawking radiation, i.e. that the mass/energy and entropy of a black hole will gradually decrease. Is there a contradiction here?

Note that I've never understood why quantum physicists seem to have such a difficult time with the prospect of information loss that they refer to it in the context of BHT as the black hole information paradox. Stuff falls in, once it does so we lose any detailed information it might have carried (leaving us only with the conserved quantities of mass/energy, angular momentum, and electrical charge), and when it is reradiated via Hawking radiation it is completely thermalized, i.e. carries no information content. What's the big deal? Information loss happens all the time, even in much more mundane contexts - for example, in fluid dynamics (what I did my PhD in), one of the most basic concepts in supersonic flow theory is that flow that goes through a shock wave suffers irrevocable information loss. In mathematical terms, there are infinitely many initial states which can give rise to a shock wave of a given character, but once the fluid passes through it, we can no longer distinguish among them, all we can say is that the initial conditions satisfied these basic conserved properties that gave rise to the shock - very similar to the no-hair theorem of BHT. In fact, entropy increase is a precise measure of information loss - as a system approaches thermal equilibrium, it carries less and less detailed information, i.e. its entropy increases. Why should black holes obey all the other rules of classical thermodynamics (with suitable account being taken of general-relativistic and quantum phenomena), but magically be immune to the one about "left to its own devices, every dissipative system tends to approach a state of thermal equilibrium"? I've never understood the supposed huge controversy there.

[xilman]

Originally Posted by ewmayer

A more interesting issue which I'll leave as an exercise for the motivated reader is: does Hawking radiation violate the second law of thermodynamics? We know from the by-now well-established theory of black hole thermodynamics (BHT) that the entropy of a black hole is proportional to the area of its event horizon, hence the more massive the black hole, the greater its entropy. On the other hand, BHT also predicts that an isolated black hole (i.e. one with no external influx of mass/energy) will slowly lose mass and "evaporate" (though on a typical timescale tremendously larger than that of the present age of the known universe) via Hawking radiation, i.e. that the mass/energy and entropy of a black hole will gradually decrease. Is there a contradiction here?

I'm not entirely sure whether I should put this response into [ spoiler] [ /spoiler] tags. Just in case I'm giving too much away, I'll give a hint sufficiently strong to convince Ernst I'm on the right track but not enough to reveal too much.

Consider the entropy of a living organism.

BTW, the "typical timescale" depends enormously on the mass of the BH, as I'm sure you are aware. A solar mass black hole certainly has a very long lifetime, not least because it is colder than 2.7K and so is gaining mass from the cosmic background radiation. On the other hand, a 1 kilotonne black hole is so hot that it evaporates in very much less than a second and makes a moderately impressive explosion. An even more extreme example: a 1 proton-mass BH, such as may plausibly be created in the LHC currently being built at CERN, evaporates in about the same time as light takes to travel across its event horizon.

Originally Posted by ewmayer

Note that I've never understood why quantum physicists seem to have such a difficult time with the prospect of information loss that they refer to it in the context of BHT as the black hole information paradox. Stuff falls in, once it does so we lose any detailed information it might have carried (leaving us only with the conserved quantities of mass/energy, angular momentum, and electrical charge), and when it is reradiated via Hawking radiation it is completely thermalized, i.e. carries no information content. What's the big deal? Information loss happens all the time, even in much more mundane contexts - for example, in fluid dynamics (what I did my PhD in), one of the most basic concepts in supersonic flow theory is that flow that goes through a shock wave suffers irrevocable information loss. In mathematical terms, there are infinitely many initial states which can give rise to a shock wave of a given character, but once the fluid passes through it, we can no longer distinguish among them, all we can say is that the initial conditions satisfied these basic conserved properties that gave rise to the shock - very similar to the no-hair theorem of BHT. In fact, entropy increase is a precise measure of information loss - as a system approaches thermal equilibrium, it carries less and less detailed information, i.e. its entropy increases. Why should black holes obey all the other rules of classical thermodynamics (with suitable account being taken of general-relativistic and quantum phenomena), but magically be immune to the one about "left to its own devices, every dissipative system tends to approach a state of thermal equilibrium"? I've never understood the supposed huge controversy there.

I never really understood that myself. As far as I do understand it, I believe the problem is not information loss but entropy loss. Here's my admittedly poor understanding.

Entropy is essentially the lack of knowledge about the state of a system. The more states something can be in without changing its macroscopic properties, the higher the entropy. Conversely, something which can only be in a few special states has very low entropy. This understanding is, so far, in accordance with your observations of the behaviour of supersonic shocks.

The difference between black holes and a classical fluid is that there are very few states a black hole can be in. The only things independently measurable, even in principle, are its mass, angular momentum and electric charge. Everything else you can measure is uniquely determined by the values of these three quantities.

Contrast this with the material having gone through a shock. You can, in principle, measure the positions and momenta of every particle in the fluid. There are a very large number of possible states which are effectively identical from the point of view of macroscopic observables.

The contrast is thus: post-shock fluid has undergone an entropy increase. Post-collapse BH has undergone an entropy decrease. Where did that entropy go? Some of it went out in radiation: electromagnetic radiation carried away electric and magnetic dipole moments (and higher multipole moments) leaving behind just the (monopole) electric charge; gravitational radiation carried away quadrupolar and higher multipolar mass distributions, leaving behind just the monopole (mass) and dipole (angular momentum) elements. The problem (and this is the crux of my poor understanding) is that the entropy carried away by the radiation is very much less than the entropy which went into the BH in the first place.


Paul

(added in edit: the result you quote, that the entropy of a BH is proportional to its surface area, is properly true only of an uncharged static BH --- a so called Schwarzschild BH. Rotating and/or charged black holes are more complicated. A consequence of this complication is that it is possible to extract energy from them by converting them into Schwarzschild BHs. Once you have a Schwarzschild BH, no more energy can be extracted. Analogues for all these behaviours should be recognizable from more familiar thermodynamical systems.

Also added: the final electric and magnetic moments are non-zero (despite what I may have led you to believe) but they are uniquely determined by the mass, angular momentum and charge of the BH --- there is no way to hide the missing entropy in them.)

[retina]

Sorry to dredge up an old topic but I think this fits here well.

If the amount of frame dragging is proportional to the spin of the singularity then I think that requires that the singularity cannot ever be zero radius. If the radius were to ever get to zero then all sorts of effects would be measurable. Most notably the infinite spin would necessarily create infinite frame dragging (since anything infinite cannot be reduced no matter how many times you divide by r²).

[xilman]

Originally Posted by retina

Sorry to dredge up an old topic but I think this fits here well.

If the amount of frame dragging is proportional to the spin of the singularity then I think that requires that the singularity cannot ever be zero radius. If the radius were to ever get to zero then all sorts of effects would be measurable. Most notably the infinite spin would necessarily create infinite frame dragging (since anything infinite cannot be reduced no matter how many times you divide by r²).

Why do you regard infinite density and as acceptable (evidenced by your use of the word "singularity") but infinite frame dragging as an unacceptable concept? Finite mass-energy can give rise to infinite density (if you believe GR) so why should finite angular momentum not give rise to infinite frame dragging?

(All this is independent of the plausible argument that GR predicts its own demise by its very insistence on the possibility of singularities.)

Paul

[retina]

Originally Posted by xilman

Why do you regard infinite density and as acceptable ... ?

I don't actually. That was my point. I don't believe the "thing creating the black hole" (I'm sorry if singularity was the wrong word to use previously) can become infinitely small (zero radius) because of the infinity problem.

[davieddy]

In my experience, enjoying physics is a matter
of finding your own depth.
Re infinity, if the universe is infinitely big, mustn't the
big bang have been likewise?

[retina]

Originally Posted by davieddy

In my experience, enjoying physics is a matter
of finding your own depth.
Re infinity, if the universe is infinitely big, mustn't the
big bang have been likewise?

For sure space can be said to be big, but there is no evidence to show that it is infinite¹. My current lack of understanding with infinities is of the very small type associated with black holes.

¹ Indeed I think that Olbers' Paradox gives a good argument to show that the universe is not infinite.