I live in the far distant future and my group of friends (myself included) decide to buy 2 used spaceships to travel to the nearest black hole and see what happens there (or just kill ourselves).

The first group leaves earth earlier than the second group, but my ship has the other ship in visual range at all times during the travel. So the question is: How can we decribe the events that I would see, from the moment that the first ship approaches the event horizon, until my own ship reaches the last tick before crossing the event horizon?

If this question was answered before, please send the link with the answer. If you don´t understand the question (english is not my first language) just ask and I will be happy to (try to) clarify).

Thanks in advance.

Just to clarify, I´m asking what should happen to the other spaceship, from my point of view, supposing we´ve kept the same acceleration relative to each other (until the black hole itself could have any meaningful effect on us).

I think you see his clock slow down while he sees your clock speed up. I'm guessing the two of you end up passing the event horizon nearly simultaneously. I estimate the chance I'm correct to be better than 10%.


PairTheBoard

Yes, it feels a little counterintuitive to me, but it totally makes sense that we should enter together.

What is a little hard to understand is: if the above is correct, can I say that all bodies, particles, ..., that entered or are going to enter the black hole at any given time, will always do so together, from my point of view (or the pov of anyone who has entered it)?

In the original post you had them in visual range all the time. In the last post you mention any body/particle ever. Guess we have a limit problem here, a Zeno paradox.

Sorry, I didn´t read the "nearly" in the post above and made the second post considering that we would cross at the same time no matter the distance between us or even the acceleration (despite what I said that we´ve kept the same acceleration).

As far as I can understand, an observer outside the event horizon can´t see anything crossing it. I understand that it´s due to the way the infinite gravity distorts the space time over there. So I will be accelerating faster and faster while the other ship in front of me, being subject to greater effects from the black hole since they are closer, should slow down (according to my own frame) until stopping. But since I´m also crossing the event horizon, we should cross at the exact same time from my pov.

The second paragraph from my second post is a mistake.

You’ll probably see the ship distort and then get incinerated in Hawking’s Inferno. No need to mourn just yet, because right after your ship is incinerated (from a hypothetical 3rd ship perspective) you’ll catch back up to the first ship, find them well and have a good laugh over the whole incident.

The infinite gravity isn't quite at the event horizon. You'll have to wait until hitting the singularity.

Forgot about the distortion (due to the fact that the ship has dimensions greater than 0 I guess?).

It has ten. Like quantum objects have a habit of having.

Ok, didn´t know.

You will likely see your friend approach but never cross horizon and then it will take forever to see him disappear past the horizon until the moment you passed also (that will happen in finite proper time though for you) (you will stop making sense of what you see from him just a little before crossing likely because its all so fast and spread out and there are not infinite number of photons emitted). After that point you will no longer see him (forward darkness) if you both follow identical radial orbits to the center. No light geodesic exists that has increasing r when inside. So light from them cannot reach you anymore unless it was radiated sideways and orbits are potentially doable like that. So you can see inside your spaceship up to a point. (how it looks inside has to be consistent with what kind of geodesics for light are allowed that cross your falling geodesic basically you intersect at lower than emitted radius or not at all.)

You will find the truth about what happens inside (that they are not correct that there is a singularity at the center by the way) after crossing the horizon when its too late to go back but all this makes sense only if we are talking a very large black hole because on any smaller ones even typical galactic ones (unless ultra huge ones with 1 bil solar masses etc) gravity and tidal forces at the horizon are enormous even if of course still finite and not singular. Therefore any human wouldn't be able to survive the event typically with a body that wasn't torn apart.


See some properties here (like check out gravity strength at horizon for even 1 bil suns black hole hence "interstellar" movie claim of realistic physics is bs moreover Kip Thorne in the team who probably should have or did protest it)

http://xaonon.dyndns.org/hawking/

The sun is 2*10^30 kgr or 2*10^27 tons.

Notice once you cross the horizon it takes 10^-5*(M/Msun) seconds to hit the singularity at the center (but which i doubt is that way so even less time to hit the "truth")

Basically the nearest black hole wont do it. Since astrophysical black holes at order 3-100 Msun often making surface gravity 1 billion g lol and time to the center only 10^-3 sec. So the concept of seeing your friend taking forever to cross the horizon isnt even registering in human senses as it all happens so fast for nearby black holes.

If you had 10^9 Ms galactic super black hole (largest speculated from observation of distant galaxies is near 10^10 suns) then it would take 2.8 hours to hit the center and at horizon gravity would be still 1000 g making it insanely tough experience.

So its not gonna happen nicely anyway and its the kind of physics that gedanken experiments are false approach usually because all kinds of phenomena take place that invalidate classic rigid horizon concepts that go about the idea that you see them freeze forever as they are crossing etc. It aint happening like any of this at all that you see in the usual books or lectures etc.

Imagine a second timelike line (ie geodesic of a massive particle) falling like the first shown here a bit later destined to also cross the horizon (say to the right of the first one). You will see from that second what lightcones of the first particle (shown here at different points) allows you to see at various points of emission (ie where it intersects your timelike geodesic - the second one that you can imagine following the first one shown above). Each cone shown here is a new emission event say and at the horizon the cone is directed parallel to horizon taking forever to reach far distant observers and once inside it, where it can not escape out anymore, all light cones point to lower r, time itself is falling to the singularity - your geodesic has finite proper time left before it crosses the singularity, it is now an incomplete geodesic -of course it will cross something more exciting below the horizon instead if i am right, something that violates Raychaudhuri's equations conditions and invalidates as a consequence the conditions of the Penrose-Hawking singularity theorems.)

https://en.wikipedia.org/wiki/Raychaudhuri_equation
https://en.wikipedia.org/wiki/Penros...arity_theorems

The second timelike curve will always see some emissions made before the first one crossed the horizon on the way to its own crossing. But it wont see anything past the horizon anymore. According to classical theory it will see the last one it saw the moment it also crosses.


To see where light emitted by the first observer (ie how it looks to you and where you are then) crosses the second timelike curve just extend the lightcones shown here from the first until they cross the other second line imagined but not drawn in the picture above. The crossing points are the events in the second observer's timelike geodesic where the emission instances are observed by the second.

For more on Penrose diagrams.

Some proper mathematical introduction to Penrose Diagrams that can help answer such kind of problems and offer intuition about what is happening.

http://www.ift.uni.wroc.pl/~blaschke...r/Felinska.pdf

https://arxiv.org/pdf/1512.02061.pdf

https://jila.colorado.edu/~ajsh/insidebh/bhfs.html

Thank you for all the resources and explanations masque de Z.

Technically yes it would "disappear" the way we define "seeing" something because radiation from something is quantized and not made of infinite light rays like the geometric construction that General Relativity is would assume with these Penrose diagram equations. So before the exact crossing something is emitted and that happens in a time before the actual crossing divergence point so not at the actual time dilation infinity point r=2M or even arbitrarily close to it. And have that added to the reality that a true black hole doesn't have a totally static horizon that is geometrically perfectly defined in strict terms as it is constantly evolving with new matter/radiation incoming.

It is true however that some photons, the last ones, that wont be enough to make sense of the "seeing something" idea, but as strictly speaking detected photons of a no longer coherent image, will reach you as you are crossing or very close to it.

The actual crossing is happening so fast actually in your frame (10^-5 M/Ms seconds is the total time to the singularity after crossing the horizon so imagine what a fraction of it before is like for even a galactic size black hole of 1 bil solar masses, probably only a second or so.

The way i imagine going into a black hole is first you see a dark hole in your field of vision that starts getting closer and closer with the universe in its boundary becoming distorted from lensing. The black region gets bigger and eventually becomes the majority of the world view perception as you are crossing. Then once inside the world is left behind in a smaller and smaller "world" hole of star lights and distant galaxies , the exact opposite of what was going when approaching the black region. (the white region is leaving you behind). Eventually all light from the outside world is reduced to a tiny spot in the "sky" and at some point after you hit a new state of matter that is yet to be discovered at CERN in quark gluon plasma experiments if i am right and that is only possible at super nuclear densities. Of course its highly unlikely that one survives the duration of that trip as a human given the tidal forces. In any case, new state of matter or singularity, the end is horrific and you cant tell to others outside the truth unless i am right and you can "influence" with your actions the object you hit inside in a way that is ultimately correlated to the Hawking radiation at the horizon! That object's equation of state would have to violate the singularity theorem energy conditions aborting further collapse to a singularity that never forms.

https://www.pitt.edu/~jdnorton/teach...ure/index.html

Why We Need a Better Diagram for Visualizing Black Holes: Conformal Diagrams

Einstein for Everyone
https://www.pitt.edu/~jdnorton/teach...410/index.html