B Do black holes determine time's arrow?

[stevendaryl]

Btw, if you were to assert this claim as an empirical claim about our actual universe,

Yes, it's a general fact about physics in a universe with time-symmetric laws. There is no notion of "future" outside of the thermodynamic arrow of time.

Or if you were to say that, yes, you can have idealized solutions in GR where there is no meaningful thermodynamics at all (for the reasons I have already described), but there is still proper time along timelike curves and there is still a physical distinction being made between corresponding pairs of solutions like "star collapsing to black hole" and "white hole exploding into star",

No, I don't think that there is a physically meaningful distinction in the absence of a thermodynamic arrow of time.

Every GR textbook I have ever read says that such a rule of physical interpretation is valid.

I don't know what you can possibly mean by "valid". Certainly, given a choice of an arrow of time, you can distinguish between a black hole and a white hole. It's relative to that choice, though.

 

[stevendaryl]

Not according to every GR textbook I have ever read. Again, if you disagree, please give me a reference that supports your claim.

I think you're misinterpreting those textbooks. They are focusing on General Relativity, not on the general problem of establishing causality in a universe with time-symmetric laws. They are assuming an arrow of time.

This is really not specifically about General Relativity. General Relativity is in the same boat as Maxwell's equations and Special Relativity. The laws of physics don't distinguish future and past (leaving out weak interactions). They don't distinguish between causal past and causal future. The word "causal" in a world with time-symmetric, deterministic laws is all about thermodynamics and entropy.

 

[stevendaryl]

The significance of the "causal past" of an event is that, with deterministic, time-symmetric laws governing the universe, everything that is needed to predict what happens at an event is determined by that event's past light-cone.

But it's ALSO true that everything that is needed to predict what happens at an event is determined by the event's future lightcone.

When the laws of physics are deterministic and time-reversible, then knowledge of the past allows you to predict the future, and VICE-VERSA. The notion of causal influences does not make a distinction between future and past.

 

[stevendaryl]

Here are lecture notes about Causal Structure of General Relativistic Spacetimes

https://www.pitt.edu/~jdnorton/teaching/GR&Grav_2007/pdf/Notes on CausalStructure.pdf

Here's a quote:

Suppose that $M, g_{ab}$ is temporally orientable. Choose one of the two possible orientations as giving the future direction of time

It goes on to define the causal structure RELATIVE to the choice of what direction is future versus past.

 

[stevendaryl]

From this paper:
http://philsci-archive.pitt.edu/800/1/The_Arrow_of_Time_in_Cosmology.pdf

The main difficulty to be encountered in answering this question lies in our anthropocentric perspective: the difference between past and future is so deeply rooted in our language and our thoughts that it is very difficult to shake off these asymmetric assumptions. In fact, philosophical discussions around the question are usually subsumed under the label “the problem of the direction of time”, as if we could find an exclusively physical criterion for singling out the direction of time, identified with what we call “the future”. But there is nothing in physics that distinguishes, in a non-arbitrary way, between past and future as we conceive them. It might be objected that physics implicitly assumes this distinction with the use of asymmetric temporal expressions, like “future light cone”, “initial conditions”, “increasing time”, and so on. However this is not the case, and the reason can be understood in simple conceptual terms...

The paper goes on to discuss the problem of defining a "cosmological arrow of time", but along the way dismisses the idea that our use of "future light cone" means by itself that there is a fundamental difference between past and future.

 

[stevendaryl]

Another quote from the above paper that is directly relevant to the discussion:

However, we know that, if t is the cosmic time, then if [hij(t, x 1 , x 2 , x 3 ), φ(t)] is a solution of the Einstein’s field equations, [hij(-t, x 1 , x 2 , x 3 ), φ(-t)] is also a solution. In other words, we obtain two solutions, each one of which is the temporal mirror image of the other, that are both possible relative to the laws of general relativity...

But why the two possible universes are different?

...
it makes no sense to say that, when we obtain two solutions of the field equations, one the temporal mirror image of the other, they describe two possible universes whose difference consists in being opposed in time: on the contrary, such solutions are different but equivalent descriptions of one and the same possible universe

 

[PeterDonis]

it's a general fact about physics in a universe with time-symmetric laws. There is no notion of "future" outside of the thermodynamic arrow of time.

I disagree. Time-symmetric laws is not the same thing as time-symmetric solutions, and the latter are what describe possible universes.

I don't think that there is a physically meaningful distinction in the absence of a thermodynamic arrow of time.

I disagree.

I don't know what you can possibly mean by "valid".

I mean that I am giving a rule of physical interpretation, and you are denying it.

Certainly, given a choice of an arrow of time, you can distinguish between a black hole and a white hole. It's relative to that choice, though.

Now I'm the one who doesn't understand what you can possibly mean. Having the singularity in your future is physically different from having it in your past. This physical difference is reflected in the theory by having two different models, each of which is the time reverse of the other. Again, I am baffled as to why you seem unable to accept this simple fact.

The notion of causal influences does not make a distinction between future and past.

In a fully deterministic theory, yes, the past can be retrodicted from the future just as the future can be predicted from the past.

However, that is a weaker claim than the one you make in the quote. The notion of "cause" does make a distinction between future and past: causes come before their effects.

You would probably say that this distinction requires a thermodynamic arrow of time; however, that is an empirical claim, not a rule that excludes any theoretical model that does not abide by it.

I'll take a look at the two references you give and comment on them in a separate post.

 

[PeterDonis]

Here are lecture notes about Causal Structure of General Relativistic Spacetimes

These notes do not discuss proper time along worldlines at all, let alone its physical interpretation.

It goes on to define the causal structure RELATIVE to the choice of what direction is future versus past.

No, it defines the terminology we use for causal structure relative to the choice of what direction is future versus past.

What it does not do anywhere, as above, is talk about actual physical interpretation. To put it another way, it does not talk at all about why you would choose which direction is future versus past. And the only specific spacetimes it discusses, Minkowski and Godel, are time symmetric, so for them it's easy to argue that the choice of future vs. past makes no difference physically. Whereas the discussion in this thread is specifically about time asymmetric spacetimes, where the choice of which direction is future vs. past does make a physical difference.

 

[PeterDonis]

From this paper:

This paper is making a proposal, not describing the standard rules of physical interpretation of GR that appear in GR textbooks.

Also, if we're going looking for quotes, how about this one:

From our perspective, it is possible to address the problem of the arrow of time in cosmology in terms of the geometrical properties of the space-time, independently of thermodynamic arguments. In this sense, we follow Earman’s “Time Direction Heresy”, according to which the arrow of time, if it exists, is an intrinsic feature of space-time “which does not need and cannot be reduced to nontemporal features” (Earman, 1974, p.20). In other words, the geometrical approach has conceptual priority over the entropic approach, since the geometrical properties of the universe are more basic than its thermodynamic properties: the definition of entropy and the calculation of the entropy curve for the whole universe are possible only if the space-time has certain definite geometrical features.

Another quote from the above paper that is directly relevant to the discussion

You left out a key part of the last snippet you quoted: "If this point is accepted, it makes no sense..." I don't accept the point referred to in the phrase I italicized (basically the previous part of the same paragraph, and the paragraph before that). This paper makes the same omission here as the other one you referenced: it does not discuss the obvious physical difference between having the singularity in your past vs. in your future; in the former case, you can see it, and in the latter, you can't. Saying that these two models are just different descriptions of the same universe makes no sense.

I think we've reached an impasse.

 

[stevendaryl]

This paper is making a proposal, not describing the standard rules of physical interpretation of GR that appear in GR textbooks.

Yes, but it reviews the current state of things when it comes to the arrow of time. The suggestion that the author is looking for a "geometric" definition of the arrow of time works exactly against the point you are making. He claims that two different solutions that are time-reverses of each other are not actually different, which is the opposite of what you're claiming.

I really don't understand your point of view, at all. And for all your call for references, you haven't posted a quote that supports your point of view.

The time-reversal of someone falling into a black hole and yelling "Help, I'm falling into a black hole!" is not someone rising from a white hole yelling "Wow! A white hole, and I'm rising out of it!". The time reversal of the first scenario is someone yelling "Help, I'm falling into a black hole!" (speaking backwards). The way to get a situation in which someone notices that they are arising from a white hole is by reversing that observer's internal sense of time, so that farther from the center seems like later, rather than earlier.

 

[stevendaryl]

What it does not do anywhere, as above, is talk about actual physical interpretation. To put it another way, it does not talk at all about why you would choose which direction is future versus past.

There is no reason, unless you introduce observers with an internal arrow of time. You say that there is a physical distinction between, say, a black hole cosmology and a white hole cosmology, but your explanations of what that distinction is are circular. There is no possibility of observing the difference unless you assume that the observer has an internal arrow of time aligned in a particular way. What looks like a black hole to one observer looks like a white hole to a time-reversed observer.

 

[PeterDonis]

I really don't understand your point of view, at all.

And I don't understand yours (more precisely, I don't understand why you are unable to see the obvious physical difference between the two solutions, star collapsing to black hole vs. white hole exploding to star), so I guess we're even.

And for all your call for references, you haven't posted a quote that supports your point of view.

As I said, I'm traveling and don't have my copies of textbooks like MTW and Wald handy. But I have already explained that the rule of physical interpretation I have been describing is what I get from reading textbooks like those. I have never seen any claim in any GR textbook that a thermodynamic arrow of time is required for the physical interpretation of proper time along a timelike worldline. The rule as I have described it is what is used throughout those textbooks. It permeates them. I am frankly baffled as to why this is not already an obvious fact to you.

The time-reversal of someone falling into a black hole and yelling "Help, I'm falling into a black hole!" is not someone rising from a white hole yelling "Wow! A white hole, and I'm rising out of it!".

Um, yes, it is. (Except for the yelling, which is not part of the models we have been discussing. You keep adding in extra features which are not part of those models, and then using those extra features to make claims about those models. That is unjustified.) Remember we are talking about two solutions which are time reverses of each other. One solution is a star collapsing to a black hole; the other, the time reverse of that, is a white hole exploding into a star. If you add an observer (or better, a mechanical device that registers proper time along its worldline--see further comments below) comoving with the matter, they fall into the black hole in the first solution, and they rise out of the white hole in the second.

The time reversal of the first scenario is someone yelling "Help, I'm falling into a black hole!" (speaking backwards).

This is adding an extra feature that is not present in the idealized models we have been discussing, and then talking as though it proves something about those idealized models. Sorry, not buying it.

The way to get a situation in which someone notices that they are arising from a white hole is by reversing that observer's internal sense of time, so that farther from the center seems like later, rather than earlier.

Here you are agreeing with me. "Reversing that observer's internal sense of time", in the idealized models we have been discussing, means reversing the direction of increasing proper time along their worldline, relative to the singularity--proper time increases away from the singularity, instead of towards it. That is how GR models the observer's "internal sense of time". And the "observer" here does not have to be conscious; it could be a mechanical clock. It could be anything that registers the proper time parameter along the curve. And for the idealized models we have been discussing, it needs to be, to avoid confusing yourself by adding extra features (like thermodynamics) that are not present in those idealized models.

 

[PeterDonis]

You say that there is a physical distinction between, say, a black hole cosmology and a white hole cosmology, but your explanations of what that distinction is are circular.

No, it isn't. See below.

There is no possibility of observing the difference unless you assume that the observer has an internal arrow of time aligned in a particular way.

In GR, you don't "assume" this, you model it as the proper time parameter along the observer's worldline. This mathematical property of the model (which direction, towards the singularity or away from it, the proper time increases) models the physical property of the observer (which, as I said in my previous post, should actually be a mechanical device to avoid confusion). Again, I am frankly baffled as to why this is not already an obvious fact to you. This is how every GR textbook I've read does it, all throughout the textbooks.

 

[PeterDonis]

The suggestion that the author is looking for a "geometric" definition of the arrow of time works exactly against the point you are making.

No, it works against the point you are making. You are basically claiming that I can't define the proper time parameter along an observer's worldline without introducing thermodynamics. The paper, correctly, recognizes, in the quote I gave, that that is not the case; proper time is a geometric parameter and can be included in a geometric model without any thermodynamics at all.

He claims that two different solutions that are time-reverses of each other are not actually different

But not based on the viewpoint in the quote I gave; the paper bases this claim on other grounds, which I have already said that I reject.

 

[Ibix]

Borrowing the Penrose diagram from figure 10 of the paper Peter linked earlier, switching a few + and - signs in the right hand copy (and I should probably have flipped the arrows on the shock wave and the event horizon but that was too fiddly), and adding a worldline with a few ticks of its proper time:

Is this argument essentially about whether those two diagrams represent distinct physical models, and/or exactly what changes are needed to make them become distinct or not distinct?

 

[PeterDonis]

The time-reversal of someone falling into a black hole and yelling "Help, I'm falling into a black hole!" is not someone rising from a white hole yelling "Wow! A white hole, and I'm rising out of it!". The time reversal of the first scenario is someone yelling "Help, I'm falling into a black hole!" (speaking backwards).

On reading this over again, it occurs to me that we might be talking past each other because we are using the phrase "time reversal" to mean different things.

In the quote above, you are using "time reversal" to mean reversing the sign of the time coordinate. (You also showed this explicitly in an earlier post but the penny didn't drop for me then, unfortunately.) You were correct earlier when you said this cannot change the actual physical situation, since of course no coordinate transformation can do that.

However, throughout this discussion, I have been using "time reversal" to mean reversing the sign of proper time along the congruence of worldlines describing observers comoving with the matter. This is a coordinate-free operation that does change the actual physical situation (for the reasons I have given in previous posts), but of course it is not the same as a coordinate transformation and it can be described without any coordinate change at all.

It does happen that the effect of both of the above operations on the relative signs of the time coordinate and proper time along the congruence of worldlines is the same (both operations flip that relative sign), but they have that effect for different reasons. That means we shouldn't be using the same term for both operations. Unfortunately, I don't have a good alternate term for either one.

 

[PeterDonis]

Is this argument essentially about whether those two diagrams represent distinct physical models, and/or exactly what changes are needed to make them become distinct or not distinct?

It might be, but after realizing what I described in my previous post just now (that @stevendaryl and I have been using the phrase "time reversal" to mean different things), I'm not sure.

In addition to the issue I mentioned in that post just now (that I don't know of a good alternate term for either operation I described, reversing the time coordinate or reversing the proper time along worldlines), there is also the issue that, in the literature, it is not clear whether, for example, the labeling of the infinities, $i^+$, $i^-$, $I^+$, $I^-$, is supposed to be relative to the labeling of the time coordinate or the labeling of proper time along worldlines. As you have drawn the diagrams, you are reversing the proper time along the red worldline (since the events labeled 1, 2, and 3 come in reverse order), which is how I would do it, and you have relabeled the infinities relative to that. That makes your second diagram a distinct physical situation, since the observer whose worldline is the red worldline has the singularity in his past instead of in his future. But as @stevendaryl has described his understanding of "time reversal", the ordering of events along the red worldline would not change (so your second diagram would not be describing a "time reversal" as he has been using the term); all that would change is the sign of the time coordinate, so the events 1, 2, 3 along the red worldline would occur at a decreasing series of time coordinates instead of an increasing series of them. (I'm not sure whether @stevendaryl would relabel the infinities as you have done as part of such a transformation.)

Another issue in this discussion, I think, has been whether what I have just described (the order in which the observer experiences events along his worldline) requires thermodynamics. The diagrams you have drawn don't, at least IMO; proper time along a worldline is a geometric parameter and does not require any thermodynamics in the model. (In the idealized situations we have been discussing, including your diagrams, there is no meaningful thermodynamics since the microstate of the entire universe is known everywhere. But of course that is a physically unrealistic idealization. Part of the issue in this discussion might be what the impact of that physical unrealism actually is or ought to be.)

 

[stevendaryl]

However, throughout this discussion, I have been using "time reversal" to mean reversing the sign of proper time along the congruence of worldlines describing observers comoving with the matter. This is a coordinate-free operation that does change the actual physical situation (for the reasons I have given in previous posts), but of course it is not the same as a coordinate transformation and it can be described without any coordinate change at all.

My claim is that choosing a sign for proper time is as much of a modeling choice as choosing a coordinate system.

The definition of proper time along a parametrized path $\mathcal{P}(s)$ is:

$\tau = \int \sqrt{g_{\mu \nu} (\frac{d \mathcal{P}}{ds})^\mu (\frac{d \mathcal{P}}{ds}})^\nu ds$

The choice of the parameter $s$ is a modeling choice; you can choose any smooth, monotonically increasing parameter you want. The choice of $s$ does not affect the magnitude of $\tau$. But the sign of $\tau$ is doubly ambiguous. First, a square-root has two possible values, so that is source of ambiguity. But even if we adopt the convention that we always take the positive square root of any positive number, the choice of $s$ affects the sign of $\tau$. Choosing $\lambda = - s$ will flip the sign of $\tau$.

If you have already made a choice for an arrow of time everywhere along the path, then you can choose $s$ so that it increases towards the future.

So I don't see how going from talking about reversing the time coordinate to talking about reversing $\tau$ makes the issues any different. The sign of $t$ and the sign of the path parameter $s$ are both modeling choices, it seems to me.

 

[stevendaryl]

So I don't see how going from talking about reversing the time coordinate to talking about reversing $\tau$ makes the issues any different. The sign of $t$ and the sign of the path parameter $s$ are both modeling choices, it seems to me.

The intuition about proper time for a path is that it is the time shown on an idealized clock traveling that path (or is related to it through a linear transformation). But because the laws of physics are time-symmetric, for any clock whose elapsed time increases along a path, there exists an initial condition for that clock so that its elapsed time decreases along the same path. "The time that clocks show" does not uniquely determine the sign of proper time, unless you assume that all clocks agree on an arrow of time.

 

[stevendaryl]

No, it works against the point you are making. You are basically claiming that I can't define the proper time parameter along an observer's worldline without introducing thermodynamics. The paper, correctly, recognizes, in the quote I gave, that that is not the case; proper time is a geometric parameter and can be included in a geometric model without any thermodynamics at all.

There are two different issues that perhaps are getting mixed up. You can certainly define "the future" to be the timelike direction away from the Big Bang, or in the case of a black hole, you can define "the future" to be toward the central singularity. But once you do that, a Big Bang and a Big Crunch are not different cosmologies. A black hole and a white hole are not different solutions. If you use geometry to determine the arrow of time, then the future is by definition the direction in which the universe is colder and less dense, and the future is the direction in which the singularity lies in a freefalling worldline. Using geometry implies that there is only one solution, not two. The author makes that point explicitly.

Alternatively, you can use thermodynamics to determine the direction of time. This is actually a more relevant and a richer definition, because it allows you to distinguish between a black hole and a white hole. A black hole is one in which the thermodynamic arrow of time points towards the singularity, and a white hole is one in which the thermodynamic arrow of time points away from it. The benefit to me of this approach is that it makes it an empirical question whether you are falling into a black hole or rising from a white hole. It's an empirical question whether we live in a Big Bang cosmology or a Big Crunch cosmology.

The third option is just to say that what you mean by a "solution of GR" is a solution to the field equations, plus an assignment of future/past direction to each timelike path. My complaint about that approach is just that unless the thermodynamic arrow of time agrees with the assignment, it's a physically meaningless choice. Observations and experiments can't determine such an arrow of time.

 

[PeterDonis]

My claim is that choosing a sign for proper time is as much of a modeling choice as choosing a coordinate system.

If by "modeling choice" you mean that we choose the model to match the actual physical behavior of a clock following the worldline, yes, I agree. I'm not sure that's what you mean, but if it's not, then I disagree. The whole point of the "modeling choice" you refer to is to make the proper time along the worldline, as a mathematical parameter in the model, match the clock time along the worldline, as a physical observable. You can't reverse the sign of the parameter in the math and keep the physical interpretation the same.

because the laws of physics are time-symmetric, for any clock whose elapsed time increases along a path, there exists an initial condition for that clock so that its elapsed time decreases along the same path.

And the way you model this changed initial condition is to change the sign of the proper time, the mathematical parameter in the model, to match the behavior of the physical clock. You can't change the clock's physical behavior and keep the mathematical parameter in the model the same; then the model no longer matches the physics.

"The time that clocks show" does not uniquely determine the sign of proper time,

Yes, it does, because that's the rule of physical interpretation for models in GR. I'm not going to budge from this position unless you can show me references from GR textbooks that say that the rule of physical interpretation of proper time is something different from what I've said.

There are two different issues that perhaps are getting mixed up.

No, that's not the problem. The problem is that you are not adopting the rule of physical interpretation that I have described. Plus you are making up your own rule of interpretation that comes from nowhere, as far as I can see:

If you use geometry to determine the arrow of time, then the future is by definition the direction in which the universe is colder and less dense

Nonsense. The Oppenheimer-Snyder model of a star collapsing to a black hole has the matter more dense towards the future. So does a collapsing FRW universe (which is what the matter region of the O-S model is a portion of). You are basically claiming that gravitational collapse cannot occur. That makes no sense to me.

Using geometry implies that there is only one solution, not two. The author makes that point explicitly.

I've already stated repeatedly that I don't buy this point in the paper you referenced, and explained why. Not to mention that, as I've already said, it's a paper stating a proposal by the author; the portion you describe is certainly not stating the standard viewpoint of physicists in GR, it's stating the author's opinions.

The third option is just to say that what you mean by a "solution of GR" is a solution to the field equations, plus an assignment of future/past direction to each timelike path. My complaint about that approach is just that unless the thermodynamic arrow of time agrees with the assignment, it's a physically meaningless choice.

In other words, you refuse to accept any idealized model that doesn't have any thermodynamics--which includes all of the idealized models we have discussed in this thread. I can't stop you from having this opinion, but I don't think it reflects any standard viewpoint among relativity physicists. It certainly doesn't reflect my viewpoint.

To state my viewpoint briefly: we have idealized models in which we model things like the increasing readings on clocks and the experience of observers of time flowing from past to future, using proper time along timelike worldlines. The relationship between proper time along timelike worldlines and other geometric parameters (such as where singularities are or the density and temperature of matter) is part of the physical interpretation of the model. Again, I'm not making this viewpoint up; I'm taking it from the GR textbooks I've read.

If we want to make a more complicated model that includes thermodynamics, then of course I agree that the thermodynamic arrow of time in the more complicated model must agree with the geometric arrow of time defined by proper time along timelike worldlines. So, for example, if we want our model to obey the second law of thermodynamics, we can't have proper time increasing along timelike worldlines towards a singularity that has zero entropy, like the singularity in the idealized Big Bang model (without inflation), which has zero Weyl curvature, or a hot, dense state with very low entropy, like the "Big Bang" state in more realistic models (where we might have an inflation epoch prior to the hot, dense "Big Bang" state, and where that state is not exactly uniform but has density and temperature fluctuations that will later on cause lead to gravitational clumping). This implies, for example, that a black hole singularity in a more realistic model that included thermodynamics would not be the idealized spherically symmetric one in the idealized Schwarzschild model, but something more like a BKL singularity, which has increasingly chaotic fluctuations of curvature and hence increasing entropy towards the singularity.

I don't have a problem with any of this. I just have a problem with claiming that idealized models that don't include thermodynamics either have no physical interpretation at all, or have a physical interpretation that can be adjusted at will.

 

[Demystifier]

Does black holes determines time's arrow?

No, it's the other way around. The statistical time arrow (of which the thermodynamic time arrow is a special case) determines the black hole.

Otherwise how to explain with time reversed objects been pushed out from black holes?

That's indeed explained by the time arrow, but it's important to understand that the statistical time arrow is a more general principle, while black hole is just one of its manifestations/consequences.

 

[Aanta]

No.
The idea that a black hole would become start to spew out matter under time reversal is a very odd one.
Since gravitation is invariant under time reversal.

Will all events be the same under time reversal then?
No alternative current will flip so that transformer coils will have opposite magnetic polarity.
But they will still work fine of course.

 

[PeterDonis]

The idea that a black hole would become start to spew out matter under time reversal is a very odd one.
Since gravitation is invariant under time reversal.

"Gravitation" is not the same as "black hole spacetime". The time reverse of an object made of matter that collapses to a black hole is a white hole expanding into an object made of matter. That means that in the time reversed solution, the matter does come out of the white hole.

What is invariant under time reversal is, in Newtonian terms, the "acceleration due to gravity". In the black hole case, the matter accelerates as it falls down into the black hole. In the white hole case, the matter decelerates as it comes upwards out of the white hole. In both cases the "acceleration due to gravity" points towards the hole.

 

[Aanta]

Hello PeterDonis
I have a hunch the OP had a quite good reason for asking the question here.
Lets flip the time arrow according to the question.

In the reversed time, the black hole event horizon is still supposed to exist.
But nothing can pass out from inside an event horizon.
According to your reasoning matter is supposedly now able to do so, but that is not the case.
Since the black hole would then by necessity not be a black hole with an event horizon.

I have a hunch this is why the OP asked about this matter.

But gravity IS invariant when the time arrow point the other direction.

If gravity suddenly would be repulsive, all objects would start to rip apart.
Would also the electroweak interaction have opposite polarity and matter would flow apart and make a diffuse mist of atoms? And the W and Z bosons rip even individual nuclei to shreds?
The answer is still no.

I will provide a most simple example.
The filament in a light bulb does not have the properties that make it possible for it to work as a solar cell, even less is it able to suck up photons from an increasingly darkening room while it convert those to electricity. So it will of course not do so if the time arrow is flipped.

 

[stevendaryl]

If you actually study the trajectory of a free-falling particle near an eternal black hole, you will see that it is completely time-symmetric. What's true is that the radial component of the 4-velocity of a particle cannot change sign while inside the event horizon. That means that if a particle falls through the event horizon (so the radial component of its 4-velocity is negative, meaning that the Schwarzschild coordinate r is decreasing with proper time), then it can never turn around inside the event horizon to have a positive radial velocity.

In order for a particle to rise out of a black hole (having a positive radial velocity), it must have ALWAYS had a positive radial velocity. This means it must have come into existence inside the event horizon, arising out of the central singularity.

A realistic black hole is not eternal. In the far past, there was no black hole, there was a cloud of gas that collapsed into a black hole. So the black hole grows by particles falling through the event horizon, and so all the particles inside the event horizon are in the first category, they can only have a negative radial velocity when inside the event horizon.

So ultimately, the time asymmetry of black holes---the fact that things fall in, but don't come out---follows from a time asymmetry in our assumed initial conditions. We assume that the black holes were formed from collapsing balls of gas. The time-reversed initial condition would assume that the black holes were always there in the far past, and the particles inside the black hole all had positive radial velocity. That's the white hole solution to Einstein's equations.

 

[PeterDonis]

In the reversed time, the black hole event horizon is still supposed to exist.

No, the time reverse of a black hole is a white hole, which has no event horizon. It has a horizon, but it's a past horizon, not a future horizon. See below.

But nothing can pass out from inside an event horizon.

A white hole horizon, as above, is not an event horizon. Things can come out of a white hole horizon just fine; but they can't go into a white hole horizon.

According to your reasoning matter is supposedly now able to do so, but that is not the case.

Yes, it is. See above.

gravity IS invariant when the time arrow point the other direction.

The "acceleration due to gravity" points in the same direction, yes; gravity is attractive in the time reversed solution as well as the original solution. But the fact that gravity's direction is the same does not mean everything is the same.

If gravity suddenly would be repulsive

Nobody is claiming that it is. You are attacking a straw man.

 

[PeterDonis]

In order for a particle to rise out of a black hole (having a positive radial velocity), it must have ALWAYS had a positive radial velocity. This means it must have come into existence inside the event horizon, arising out of the central singularity.

This is impossible inside an actual black hole. But in the time reverse of a black hole, namely a white hole, this is indeed what happens: the particle comes from the white hole singularity (which is not the same as the black hole singularity) and emerges from the white hole horizon (which, per my post #117, is not an event horizon since it is a past horizon, not a future horizon).

In the maximally extended Kruskal-Szekeres geometry, both a black hole and a white hole are present, and they are not the same; they are different, distinct regions of the spacetime. That solution itself is fully time symmetric.

However, in the more realistic case of a black hole that forms by gravitational collapse of a massive object, that solution is time asymmetric, as you say, and its time reverse is another time asymmetric solution, a white hole that expands into a massive object.

Note that I am using "time reverse" here in the way I explained in earlier discussion in this thread.

 

[PeterDonis]

If you actually study the trajectory of a free-falling particle near an eternal black hole, you will see that it is completely time-symmetric.

Note that the only possible meaning for "eternal black hole" here is actually the maximally extended Kruskal-Szekeres geometry; no other "black hole" is eternal. And, as I noted in post #118 just now, in that geometry, there are two "hole" regions, not one: there is a black hole region and a white hole region, and they are not the same. So while it is possible to have a fully time symmetric trajectory for a free-falling particle in this geometry, any such trajectory will start on the white hole singularity, emerge from the white hole horizon, rise to some maximum altitude in the exterior region, fall back inside the black hole horizon, and end on the black hole singularity. It will not fall back into the same region of spacetime from which it emerged.

 

[Dale]

If gravity suddenly would be repulsive, all objects would start to rip apart.

As already mentioned, time reversed gravity is still attractive, but a time reversed black hole horizon is a white hole horizon.