Black Hole information paradox and evolution in time

[gerald V]

I refer to a Schwarzschild Black Hole as the simplest example, and a well defined time outside the hole, say the Schwarzschild time.

The information paradox of BH deals with the question of what stuff has fallen into the hole, but I am not aware that it deals with the question when the respective stuff fell in.

Why isn’t the full history of the hole a matter of considerations in the context of the BH information paradox? Or is it?

 

[PeterDonis]

The information paradox of BH deals with the question of what stuff has fallen into the hole, but I am not aware that it deals with the question when the respective stuff fell in.

A Schwarzschild black hole does not change with time, so there is no "when".

 

[gerald V]

Thank you very much. Please forgive my complete confusion.
Let us focus on those BHs which actually do grow like the one which swallowed another, sending out the gravitational waves detected by LIGO. It can well happen that this hole will swallow a further one in the future. Or it can swallow other stuff like a Neutron star. At any such event, graviational waves will be sent out and will be received by LIGO (I am aware that the sensitivity of LIGO will be too low in many cases, but I am referring to the principle). Hence, there is a pattern of what the hole swallowed when, at least in Earth receive time. So I do not understand at all why in the BH Information paradox time does not play a role.

 

[PeterDonis]

there is a pattern of what the hole swallowed when, at least in Earth receive time

There also is in what might be called "hole time", i.e., in coordinates that aren't singular on the horizon (Schwarzschild coordinates, which are basically what we are using in "Earth time", are singular there). The different things that fall into the hole (except for the black hole merger, see below) cross the horizon at different events, and those events have an invariant time ordering.

When two black holes merge, however, it is not the case that one hole falls through the horizon of the other. The two horizons merge into one. That can't be described in the simple way that ordinary objects falling into the hole can; for one thing, in this case the "hole coordinates" that I referred to above don't exist, at least not in the simple form that they exist for a single hole with ordinary objects falling in. So the black hole merger case really needs to be considered separately. And that case isn't relevant to the information paradox anyway, since no ordinary objects are involved and nothing falls through a horizon.

I do not understand at all why in the BH Information paradox time does not play a role.

Because the information paradox applies to a single ordinary object falling into a single Schwarzschild hole. There is no need to consider multiple objects falling in at different times; that just adds extra complexity without changing the paradox at all. And the paradox for a single ordinary object falling into a single hole is independent of when the object falls in.

 

[Grinkle]

Because the information paradox applies to a single ordinary object falling into a single Schwarzschild hole.

If a neutron star fell into a black hole, would that potentially cause a detectable gravity wave and bring relevance to the OP's question?

 

[PeterDonis]

If a neutron star fell into a black hole, would that potentially cause a detectable gravity wave

Possibly, yes.

and bring relevance to the OP's question?

How? The star falling in--i.e., a single object falling in--already raises all of the issues involved in the information paradox, even if there is no gravity wave emitted and no other object ever falls in. And this is true regardless of when the neutron star falls in.

 

[jartsa]

The world line of a black hole has some bumps that tell us when and where something hit the black hole.

If information is conserved, then the shape of any world line must not be forgotten. Elementary particles do not remember their world lines, every electron would be different if that was true. So it must be the environment of an electron that remembers the world line of an electron.

Let's say a very small black hole has a very complex world line. The environment of the black hole must contain most of the information of the world line, as not very much information can be stored in a small black hole.

Now if that black hole sucks most of it's environment into itself, then it also sucks into itself the information about its own world line.

 

[PeterDonis]

The world line of a black hole

There is no such thing. A black hole is not a point particle or an ordinary object. It is spacetime geometry.

The rest of your post just builds on this error. It also is bordering on personal theory. Please bear in mind the PF rules in this respect.