black hole question

[hoola]

while it is presumed that information is not lost when matter falls into a black hole, it seems understood that overall mass is lost when black holes merge. What happens to the information contained within this "lost" mass due to it's conversion into the wave energy? Is this not lost, or can be somehow reconstructed from the waves, as they extend across space, or perhaps resurrected from space/time itself after the waves have passed?

Edited May 9, 2022 by hoola
spelling

[Markus Hanke]

On 5/9/2022 at 7:41 AM, hoola said:

What happens to the information contained within this "lost" mass

To understand this, you have to remember how the “M” parameter enters into the black hole metric in the first place. What happens is that, because the Einstein equations are differential equations, you need to provide boundary conditions in order to obtain any particular solution; for the case of Schwarzschild spacetime (I presume this is what your question is referring to), one of these boundary conditions is asymptotic flatness - meaning that, sufficiently far away from the black hole, gravity behaves like a Newtonian inverse square law. Matching up the proportionality constants thus introduces the parameter “M”, which, accordingly, is interpreted as total mass. It’s important to realise though that this is a property of the entire spacetime, not just of any particular subregion.

Now, if you reduce the event horizon area of the black hole and in its stead add a gravitational radiation field in just the right way, this will still be true - the “overall curvature” of the entire spacetime is in some sense a conserved quantity. It will only be distributed differently, and the new metric will be something more complicated than Schwarzschild. But nothing will be lost as such. The information loss paradox arises only once we consider quantum effects at the event horizon, but not in the purely classical realm of GR.

[hoola]

It seems you are saying that the waves are indeed carrying away and thus preserving the information into the "entire" spacetime (universe)

[Markus Hanke]

22 hours ago, hoola said:

It seems you are saying that the waves are indeed carrying away and thus preserving the information into the "entire" spacetime (universe)

In a way, yes.

To be more precise - if you know all relevant details of the radiation field, you can reconstruct the masses of the two black holes prior to their merger. This is how gravitational wave observatories know the approximate masses of objects undergoing a merger. So the information is preserved in this sense.

[beecee]

On 5/10/2022 at 4:14 PM, hoola said:

It seems you are saying that the waves are indeed carrying away and thus preserving the information into the "entire" spacetime (universe)

 

On 5/10/2022 at 3:22 PM, Markus Hanke said:

Now, if you reduce the event horizon area of the black hole and in its stead add a gravitational radiation field in just the right way, this will still be true - the “overall curvature” of the entire spacetime is in some sense a conserved quantity. It will only be distributed differently, and the new metric will be something more complicated than Schwarzschild. But nothing will be lost as such. The information loss paradox arises only once we consider quantum effects at the event horizon, but not in the purely classical realm of GR.

The first gravitational wave detction by aLIGO was between a 29 solar  mass BH and a 36 solar mass BH The final merged BH after ringdown was a 62 solar masses. 3 solar masses lost  with gravitational radiation. This was designated GW150914.

https://aasnova.org/2016/02/11/ligo-discovers-the-merger-of-two-black-holes/

https://www.ligo.caltech.edu/news/ligo20160211

https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves#GW150914_event

 

[geordief]

6 hours ago, Markus Hanke said:

In a way, yes.

To be more precise - if you know all relevant details of the radiation field, you can reconstruct the masses of the two black holes prior to their merger. This is how gravitational wave observatories know the approximate masses of objects undergoing a merger. So the information is preserved in this sense.

Can information ever be preserved  in such a way as to reconstruct a previous system from a system that has evolved ?(not necessarily  relevant to black holes maybe  and I wonder if I have misunderstood  the information question)

 

It seems to me that if we cannot predict the future  in any exact way then the past  is exponentially  more impossible to do so.

 

Is information not being lost all the time?(or is/was the information paradox about the possibility or not to retrieve any trace at all of the configuration of systems  that had gone into a Black Hole)?

[MigL]

As Markus explained, classical GR is deterministic.
Knowing all initial conditions allows the prediction of future conditions, like a clockwork.
And present conditions can be extrapolated back into the past.

Quantum effects throw a 'wrench' into the classical works.
For a BH this would be most evident near the predicted singularity, and at the boundary we call the event horizon, where information loss difficulties arise.

[Markus Hanke]

18 hours ago, geordief said:

Can information ever be preserved  in such a way as to reconstruct a previous system from a system that has evolved

Yes - this is in fact a fundamental symmetry of nature, called unitarity. Colloquially speaking, information should be conserved when a system evolves, at least in principle. There is of course a precise mathematical definition for this, but for now you get the idea.
For example, if you burn a book, the information contained therein becomes inaccessible for all practical purposes; however, if you somehow knew everything there is to know about the final state of the burning, ie all details of every single ash particle left behind etc, then in principle it would be possible to reconstruct the original book, so the information has been preserved, albeit in different form. Unitarity is very important particularly in quantum mechanics. Crucially, the black hole information paradox would be an example where unitarity is violated - this is why it is so problematic, and requires resolution.

18 hours ago, geordief said:

Is information not being lost all the time?

No, ordinary physical processes should be unitary, ie information only changes its “form” and “location”, so to speak.

18 hours ago, geordief said:

or is/was the information paradox about the possibility or not to retrieve any trace at all of the configuration of systems  that had gone into a Black Hole

In the BHIP, information enters the event horizon. Quantum field theory combined with GR tells us that the event horizon carries entropy and radiates; this Hawking radiation is perfect black body radiation and thus carries no usable information. At the same time, the BH shrinks and eventually evaporates completely, leaving no remnant other than its Hawking radiation. The final state of BH evolution is thus simply a black body radiation field that contains no relevant physical information - meaning it is impossible to reconstruct whatever information entered the event horizon previously, based on what’s left of the original BH. The information is lost, not just for practical purposes, but also in principle - a violation of unitarity.

16 hours ago, MigL said:

Knowing all initial conditions allows the prediction of future conditions, like a clockwork.

As a side note - in practice (as opposed to in principle) determinism does not imply predictability. For example, a GR 3-body problem is fully deterministic, but in general only predictable for limited amounts of time (Lyapunov time), due to chaotic dynamics. 

Edited May 12, 2022 by Markus Hanke