Merging black holes: gravitational waves and information

[arusse02]

A popular theory is that black holes gradually leak information because of black hole evaporation due to hawking radiation. When black holes merge, a significant portion of their mass is converted into gravitational waves. If it's true that black holes leak information due to hawking radiation, then how is the information preserved in the gravitational waves produced by the merger of two black holes? There doesn't seem to be any reasonable mechanism by which these gravitational waves could contain the information that would have otherwise been leaked due to hawking radiation. According to relativity, the gravitational waves are purely a result of the masses of the black holes and their distance apart.

It seems like all that information is lost in gravitational waves if we assume that black hole evaporation is the correct solution for the black hole information paradox.

 

[jartsa]

Two black holes fuse, the resultant black hole is colder than the original black holes.

Less energy is needed so store the same information when temperature has decreased. Temperature here is the temperature of the information storage thing.

So the answer is: The information in the two black holes went into the new black hole. Just a small amount of information is in the gravitational waves.

Or we could say that there is a pair of objects, and some of their potential energy gets converted to gravitational waves. That is a quite normal thing to happen. But these objects happen to be special in that they separately contain the maximum amount of entropy Q/T. For these objects the resultant object has to have a lower temperature than the original objects, so that the resultant object is able to contain the information of the original objects even while containing less energy than the original objects together.

Oh, I used a wrong entropy formula again, check the correct one from here:
https://www.physicsforums.com/threa...-a-fraction-of-heat-over-temperature.1007259/

 

[Dale]

There doesn't seem to be any reasonable mechanism by which these gravitational waves could contain the information

Why not? EM waves clearly can contain information. What would prevent gravitational waves from containing information?

 

[vanhees71]

To the contrary gravitational waves provide a lot of information. That's why all astrphysicists are so enthusiastic about the possibility to observe gravitational waves accurately. For black-hole mergers you can deduce at least the information on their masses. For neutron-star mergers we have another important key to learn about the equation of state of strongly interacting matter. If you look just for papers of the first neutron-star merger, you get tons of information on such "kilonovae". It's also the most impressive example for "multi-messanger astronomy", i.e., where the NS-merger events was observed through the gravitational-wave signal as well as by many observations over a large range of the electromagnetic spectrum. All this information together leads to completely new insights, and there'll be much more to come in the near future!

 

[Dale]

In principle I would think that a GW must be able to carry more information than an EM wave due to the additional polarization states. Of course, that is not information we could capture at this time, but it seems to be a physical channel for information.

EDIT: I made a mistake here, see below

 

[vanhees71]

That's an interesting idea, but what do you mean by "additional polarization states"? As a massless spin-2 field a GW has two independent polarization states as em. waves. Another interesting question is, how one can technically measure the polarization of a GW.

 

[Dale]

That's an interesting idea, but what do you mean by "additional polarization states"? As a massless spin-2 field a GW has two independent polarization states as em.

Oops, yes you are right. The "plus" and "cross" polarization states are still just two polarization states. I was just thinking that they were more complicated than "horizontal" and "vertical", but being more complicated doesn't mean that there are more of them. My mistake.

 

[vanhees71]

Nevertheless, do you have an idea, whether the GW experimentalists have ideas how to measure the GW polarization? I guess in principle there should be information about the sources also in the polarization.

That's also clear in the analogous case of em. waves, e.g., the fluctuations of the polarization of the cosmic microwave background radiation contains further information in addition to the temperature fluctuations:

https://en.wikipedia.org/wiki/Cosmic_microwave_background#Polarization

 

[jartsa]

Why not? EM waves clearly can contain information. What would prevent gravitational waves from containing information?

Yes but OP knows (somehow) that gravitational waves do not contain as much information as Hawking radiation with the same energy contains. Which is true, except maybe in some very special cases. Then OP suspects that that means that large amount of information must go missing when large amount of gravitational waves are generated in a black hole collision.

 

[Dale]

Yes but OP knows (somehow) that gravitational waves do not contain as much information as Hawking radiation with the same energy contains. Which is true, except maybe in some very special cases.

Is it true? I would think that there is lots of information there. Just because we cannot yet measure that information doesn't mean it isn't present.

Of course, your points about temperature are valid. So even if the OP's premise is correct there is a clear and simple resolution, but I just am not at all convinced about the premise in the first place.

 

[PeterDonis]

do you have an idea, whether the GW experimentalists have ideas how to measure the GW polarization?

Yes; that's why the LIGO system has multiple detectors with different spatial orientations. By combining the outputs from multiple detectors, you can obtain a waveform for each of the two orthogonal polarizations.

 

[PeterDonis]

According to relativity, the gravitational waves are purely a result of the masses of the black holes and their distance apart.

No, this is not correct. The details of the gravitational waves emitted from a black hole merger depend on the details of the merger: the detailed orbits of the holes as they spiral inward, the detailed changes in spacetime curvature as they merge, and the detailed changes in the shape of the horizon of the resulting hole as it "rings down" to a stationary state. There is a lot more information there than just the masses of the holes and their distance apart.

 

[jartsa]

Is it true? I would think that there is lots of information there. Just because we cannot yet measure that information doesn't mean it isn't present.

Is this a good way to show that it's true:

If we surround a black hole merger with a sphere consisting of 10²⁶ LIGOs, every LIGO receives the same info. Correction: Not the same info but there is a lot of correlation in what the LIGOs receive, in other words there is redundancy.

If we surround that sphere with a bigger sphere of LIGOS and the bigger sphere with even bigger sphere, and so on, then we can absorb all the energy that was released as gravitational waves. That energy would be huge. The amount of information would not be so huge because of the aforementioned redundancy.There's no redundancy in Hawking radiation, it looks perfectly random.