Quick question about being inside a Black Hole

[max-greece]

i am inside a Black Hole. I am travelling through time towards the end of time (as I have understood it). Does that mean, therefore, that it is not a case that I cannot escape from the event horizon it is that I cannot take a "step" towards it as that would be travelling backwards in time?

Note: I have chosen Graduate as the prefix - no idea if that refers to the level of the question or the questioner themselves. Not a physics graduate - but I am 62 so high schooler seems inappropriate.

 

[Ibix]

Not exactly - there are directions inside a black hole that are in some sense towards the event horizon. The problem is that when you are inside of the hole the event horizon recedes from you at the speed of light, so you can never catch it.

The event horizon is one of those weird things that can only do what it does in curved spacetime. It's what's called an "outgoing null surface", which means that falling through it is easier described as it passing upwards through you at the speed of light, and if you emit a light pulse backwards as it passes it'll keep up with the horizon and "hover" there forever. (In principle, anyway. This is like trying to balance a pencil on its point - possible in theory, but it's an unstable situation and any disturbance will knock the light into the hole). But that doesn't mean that the event horizon is expanding - its area remains constant unless you drop more matter in.

 

[Matterwave]

As I understand it, the prefix is supposed to say what level of answer you want. So by selecting Graduate, you are asking for an answer at the level explained to a graduate student in physics.

 

[max-greece]

Thank you for that - but I am not sure I can make sense of what you just said.

"There are directions that are, in some sense, towards the event horizon"?

"the event horizon recedes from you at the speed of light" so if the horizon is not expanding further (nothing else has fallen in) then I am traveling inwards at the speed of light? Even though I have mass?

 

[max-greece]

Thank you Matterwave. That makes sense. There should be an option for "Monkey with a Stick" that would probably be better suited to me.

 

[Ibix]

"There are directions that are, in some sense, towards the event horizon"?

Sure. Imagine two people falling through the horizon, connected to each other by a rope. When one has fallen through but the other hasn't yet, the rope leads back through the horizon. So that's a direction towards the horizon. Trouble is, the horizon is receding at the speed of light, so you can't get closer to it even if you accelerate in that direction with arbitrarily powerful rockets.

"the event horizon recedes from you at the speed of light" so if the horizon is not expanding further (nothing else has fallen in) then I am traveling inwards at the speed of light? Even though I have mass?

No, you aren't travelling at the speed of light. As you say, this is impossible for a massive object. The horizon is travelling outwards at the speed of light. It just doesn't get any bigger. This is one of those things that's only possible in curved spacetime, and I'm afraid I don't know of a good analogy for in more familiar circumstances.

 

[max-greece]

So that's a direction towards the horizon.

It is a direction but not one I can travel. In my time line towards the local end of time its part of my history. I don't think that contradicts the intial statement. When the second object passes through the event horizon (assuming the rope held) neither end could use it to pull together as the rate of progress towards the end of time is fixed and the farther back end is behind in the timeline.

 

[Matterwave]

I think there is some sense in which OP is (loosely) right.

Inside the event horizon the Schwarzschild radial coordinate, the one where $r=0$ is the singularity and $r=2M$ is the event horizon, turns time like. So in that sense, the singularity is to your future while the event horizon is to your past. So "pointing at the event horizon" would read like "pointing to the past" and indeed, unless you think like Gatsby, you can't go back there.

But it is also right that things can still follow you into the black hole. And if you can see a patch of the night sky, you could also in some sense be justified in saying the direction towards that patch of sky is the direction towards the horizon (but of course, such light is still coming from your causally connected past).

The really unfortunate thing is "the end of time" is only a finite proper time away from you once you fall through.

 

[Ibix]

It is a direction but not one I can travel.

You can travel in that direction. For an everyday analogy, say I'm walking along the road and a car passes me at 60mph. If I face its taillights, I'm walking towards it. I just can't catch it - the distance opens too fast.

When the second object passes through the event horizon (assuming the rope held) neither end could use it to pull together as the rate of progress towards the end of time is fixed and the farther back end is behind in the timeline.

Not necessarily - it depends how long the rope is compared to the scale of the black hole. You can pull together initially if the rope is reasonably short (even kilometres long for something like a supermassive black hole), but spaghettification will overcome this at some point before the singularity.

 

[Ibix]

I think there is some sense in which OP is (loosely) right.

Very loosely, although I take your point.

The problem is that "pointing in a direction" defines a 2d worldsheet (idealising your arm as a 1d line, extended in time), and there are spacelike extensions of vectors in that plane that pass through the horizon (so you are pointing at the horizon - e.g. along constant Kruskal-Szekeres time coordinates) and spacelike extensions that don't (so you aren't pointing at the horizon, you can't do that - e.g. along constant Schwarzschild interior time coordinates). I suspect some of both sets are geodesics, although I haven't checked.

The problem with the "event horizon is in the past" is exactly what you note - talking about later horizon crossings and exactly where all those stars you can see are now. Also note that the interior of the black hole is of infinite size in that scheme.

Fundamentally, black holes defy ordinary language descriptions. There's always something that "doesn't make sense" because flat (or weakly curved) spacetime intuitions aren't valid.

 

[max-greece]

I am about to take a huge risk in exposing quite how dumb I really am. On the other hand I already identify as a monkey with a stick so how shocking can that be?

A Black Hole is not like anything else in the Universe (that we know of). It is also the ultimate Black Box in terms of what the universe sees of it. Suppose that the change is even more fundamental than we appreciate. I have to admit that my first thought was "Black Holes break space-time." Maybe it does, maybe its a phase change from SpaceTime to TimeSpace or even that the Space part breaks and the Black Hole is a bubble of Pure Time. In any event it would not be unreasonable to assume that GR would no longer provide an explanation of what is happening in the Black Hole (try not to laugh).

If we were to consider the Pure Time model as it is probably the simplest then one would expect the explanation of what is happening in a Black Hole to also be simpler:

Per my original post I am travelling through time to the Local End of Time. I can only travel in a single direction following my arrow of time.

Conversely there is an end of time - where all timelines meet. At the end of time all possible directions are back in time. This is caused by the fact that Time itself is unlimited whilst the volume inside a Black Hole is not.

It means that the local end of time is an entirely geometric formation. The body that sits at the end of time is not the end of time itself - its merely in the location (more properly state) of the end of time.

Now when a Black Hole forms it does so BEFORE the singularity. The geometry of the Black Hole forms immediately. The hugely dense (but not infinitely dense) body is at the local end of time.

Now as we are at the end of time that body can never become a singularity as there is no time in which such a transformation can occur.

Further, as the arrow of time is doing our heavy lifting here, the role of gravity within the volume bounded by the event horizon, is negligible. In other words as I am approaching the end of time I will not experience any gravitational pull because, relative to the end of time, I am in the past and gravity does not travel backwards in time. The dilation of time would also not be apparent to me in local time it would only be theoretically apparent to an external observer which is not something that can exist as we are in a Black Hole.

When I come to rest at the end of time the definition of the end of time (no available direction of travel is open to me that is not backwards in time) means that the end of time expands (just as the event horizon did when I first fell in). As I am at the end of time no further change can happen to me (like being crushed by gravity).

In summary the singularity never forms and information is preserved.

Now I realise this is a big ask but be as kind as possible to the monkey and tell me, not in terms of GR, in terms of observations and implications, why this idea has to be wrong. I am now building up the courage to press the reply button.

 

[Ibix]

I'm afraid all observations are numbers, when it comes right down to it. That's why our theories are all mathematical at their core, because they have to relate one observation, one number, to another.

We believe what we believe about the interiors of black holes because they are a prediction of a mathematical model which has been validated against numbers we can observe, with careful checking against limits of observational precision. If you don't have a mathematical model, you have nothing that can be confirmed or denied. To put it bluntly, it doesn't even rise to the level of being wrong.

That last is why discussion of personal theories is explicitly against site rules.

 

[max-greece]

Oh dear - I have broken the rules already. Apologies.

 

[berkeman]

Thread closed for Moderation.

 

[berkeman]

Since this thread is based on personal speculation by the OP, it will remain closed.