Hi again shminux, this is my second question. First, I’m sorry if it’s going to be long-winded, I just don’t know enough to make it shorter :-)

It might be helpful if you can get your hands on the August 3 issue of Science (since you’re working at a university perhaps you can find one laying around), the article on page 536 is kind of the backdrop for my questions.

[Note: In the following, unless specified, there are no non-gravitational charges/fields/interactions, nor any quantum effects.]

(1) If I understand correctly, when two black holes merge the gravity waves radiated carry the complete information about (a) the masses of the two BHs, (b) their spins, (c) the relative alignment of the spins, and (d) the spin and momentum of the system, i.e. the exact positions and trajectories before (and implicitly during and after) the collision.

This seems to conflict with the “no-hair” theorem as well as with the “information loss” problem. (“Conflict” in the sense that I, personally can’t see how to reconcile the two.)

For instance, the various simulations I’ve seen of BH coalescence clearly show an event horizon that is obviously not characterized only by mass and spin. They quite clearly show a peanut-shape event horizon turning gradually into an ellipsoid. (With even more complicated shapes before, although there always seem to be simulation artifacts around the point where two EHs become one in every simulation I saw.) The two “lobes” of the “peanut EH” seem to indicate “clearly” that there are two point masses moving inside, which seems to contradict the statement that you can discern no structure through an EH.

(In jocular terms, I’m pretty sure one can set-up a very complex scenario involving millions of small black-holes coalescing with a big one with just the right starting positions that the EH actually is shaped like hair at some point during the multi-merger. I realize that’s abusing the words, but still, what is the “no-hair theorem” talking about, given that we can have EHs with pretty much arbitrary shape?)

In the same way, I don’t quite get the “information loss paradox” either. Take the simple scenario of an electron and a positron annihilating: in come two particles (coincidentally, they don’t have “hair” either), out come two photons, in other words a “pair” of electromagnetic waves. (Presumably, gravity waves would be generated as well, though since most physics seems to ignore those I presume I’m allowed to, as well.) There are differences, but the scenario seem very similar to black hole merger. Nobody seems to worry about any information loss in that case—basically, there isn’t, as all the information is carried by the leaving EM waves—so why exactly is it a problem with black holes? That is, what is the relevant difference?

[Note: if electrons and annihilation pose problems because of quantum effects, one can make up a completely classical scenario with similar behavior, using concepts no more silly than point masses and rigid rods. I just picked this example because it’s easy to express, and people actually think about it so “why don’t they worry about information loss” makes sense.]

(2) As far as I understand, exactly what happens in (1) also happens when something that is not a black hole falls into one. Take a particle (an object with small mass, small size but too low density to have an EH of its own, no internal structure other than the mass distribution inside it) falling spirally into a BH. AFAIK, this will generate almost exactly the same kind of gravitational waves that would be generated by an in-falling (micro-) black-hole with the same mass, with the only difference being that the waves will have slightly different shape because the density of the falling particle is lower (thus the mass distribution is slightly fuzzier).

Even though the falling particle doesn’t have an EH of its own, AFAIK the effects will be similar, i.e. the black hole’s EH will also form a small bump where the particle hits it, and will then oscillate a bit and radiate gravitational waves until it settles. Like in case (1) above, all the information regarding the particle’s mass and spin should be carried by the gross amplitude and phase of the waves, and the information about the precise shape of the particle (how its mass distribution differs from a point-mass like a micro–black hole) should be carried in the small details of the wave shapes (the tiny differences from how the waves would look if it were a micro–black hole that fell).

(3) Even better, if the particle and/or black hole also has electric charge, as far as I can tell the electro-magnetic field should also contain waves, similar to the electron/positron annihilation mentioned above, that carries all relevant information about electro-magnetic state of the particles before, during and after the “merger” (well, accretion in this case) in the same way the gravitational waves carry information about mass and spin.

So, as far as I can tell, coalescence and accretion seem to behave very similarly to other phenomena where information loss isn’t (AFAIK) regarded as an issue, and do so even when other forces than gravity are involved. In other words, it seems like all the information is not lost, it’s just “reflected” back into space. I’m not saying that it’s not an issue and all physicists are idiots, I’m just asking what is the difference.

(I have seen explanations of the information loss paradox that don’t cause my brain to raise these questions, but they’re all expressed in very different terms—entropy and the like—and I couldn’t manage to translate in “usual” terms. It’s a bit like using energy conservation to determine the final state of a complex mechanical system. I don’t contradict the results, I just want help figuring out in general terms what actually happens to reach that state.)