Black holes

[JebKeb]

I'm back for a short stint to clear stuff up. Hi.

We seem to have been told that the escape velocity of a black hole at a certain altitude reaches the speed of light. But if the escape velocity is the speed of light, what stops us from being in orbit around a black hole, dipping our periapsis through the event horizon and recording data, then after exiting the event horizon at a higher altitude escape the black hole where the escape velocity is manageable?

Or is the orbital velocity at that altitude faster than the speed of light? Has it been an issue of semantics?

If things get heavier the faster we go could we plunge towards a black hole, reach the same mass as one near the speed of light, and become a black hole? Or would we sling the black hole away at high speed? What would happen?

I'll post more badly formed questions a bit later once I think of some

[0111narwhalz]

I think you could probably escape a black hole by accelerating, if not for the whole time dilation thing, just as you can escape the Earth at 2m/s if you boost the whole way. You would need to stage continually, but that's engineering.

Edited March 24, 2017 by 0111narwhalz

[sevenperforce]

Good question, actually. The answer is that the space around a black hole is so aggressively curved that you would have to be traveling at the speed of light in order to orbit anywhere near the event horizon. Recall that the speed of a circular orbit increases as you move closer to the center of a body. For black hole physics, the speed of a circular orbit exceeds c well above the event horizon.

Calculating orbits near Earth is straightforward enough, but orbital mechanics goes haywire near a black hole. The reason stable orbits exist around the Earth is that Earth's gravity curves space just enough that a "straight" line closes into a loop. But a black hole curves space until there are no closed paths. If you were just outside the event horizon and tried to accelerate away, you would experience space literally stretching out away in front and behind you. The event horizon itself is where gravity drag goes to infinity. 

Finally, relativistic mass appears only from an outside reference frame. You do not experience yourself becoming more massive as you gain speed, because you are at rest relative to yourself.  

[WinkAllKerb'']

https://en.wikipedia.org/wiki/Judo

lately i do wonder if what we observe from here or there is not related to the universe shape in itself, and is may be more truncated than what we may think, also the general way it (could) move in it's own referential and a/some larger referential near the/it's "pole" could may be be used to get some "whatever" "emissive"/"missing emmissive"(/or emissive repart along the frag grenade principle near specific location and sub orbital rectiligne trajectory) back ... srry approx english

Edited March 24, 2017 by WinkAllKerb''

[YNM]

Its... not as simple as you've thought.

1. Orbits in GR are NOT periodical, despite the ability to choose a convenient coordinate (probably time-dependent) to allow one such thing. But of course the horizon will also change, in case of your question... I think we all can agree that you can't just do that, feel free to wrangle yourself with EFE.

2. Carrying information from inside a black hole... that's not quite possible. Hawking radiation is real*, but it contains no information of what's inside the whole thing; after all, it was only thanks to "spontaneous" fluctuations, so unless you want your probe to simply be torn and slowly released as an unintelligible garble of fundamental particles, in any way it's impractical and useless.

 

* as real as the set of real numbers wrt natural numbers

Edited March 24, 2017 by YNM

[HebaruSan]

2 hours ago, JebKeb said:

We seem to have been told that the escape velocity of a black hole at a certain altitude reaches the speed of light. But if the escape velocity is the speed of light, what stops us from being in orbit around a black hole, dipping our periapsis through the event horizon and recording data, then after exiting the event horizon at a higher altitude escape the black hole where the escape velocity is manageable?

Or is the orbital velocity at that altitude faster than the speed of light? Has it been an issue of semantics?

All world lines inside the event horizon lead toward the singularity. Space-time is so severely curved that time and space exchange roles in some sense; rather than helplessly move future-ward in time as you do in normal space, you now helplessly move downward toward the singularity.

A periapsis is a point in a periodic repeating elliptical path. If you dip your path inside the event horizon, then you no longer have a periapsis, because you no longer have a repeating elliptical path.

[Green Baron]

7 hours ago, JebKeb said:

what stops us from being in orbit around a black hole, dipping our periapsis through the event horizon and recording data, then after

Relativity. For the outside observer your ship stands still as reaches the event horizon. For you in the ship time dilates so much that the universe will be gone in a blink. You.can.not.return.

Apply the formula for time dilation. The moment just before v becomes c.

Edit: well, "you" might leave it as part of the hypothetical hawking radiation over the course of the next fantastillion years.

Edited March 24, 2017 by Green Baron

[Delay]

On 24.3.2017 at 1:51 AM, JebKeb said:

We seem to have been told that the escape velocity of a black hole at a certain altitude reaches the speed of light. But if the escape velocity is the speed of light, what stops us from being in orbit around a black hole, dipping our periapsis through the event horizon and recording data, then after exiting the event horizon at a higher altitude escape the black hole where the escape velocity is manageable?

If I understand correctly, you imply an elliptical orbit whose periapsis dips below the event horizon

You seem to forget about special relativity, which states that nothing with mass can go faster than light. Going back up inside the event horizon would require faster than light speeds. You would just slowly spiral to your doom because of this.

Edited March 25, 2017 by Delay
Addendum

[sevenperforce]

20 hours ago, Delay said:

If I understand correctly, you imply an elliptical orbit whose periapsis dips below the event horizon

You seem to forget about special relativity, which states that nothing with mass can go faster than light. Going back up inside the event horizon would require faster than light speeds. You would just slowly spiral to your doom because of this.

I don't think he realized the periapsis velocity would be superluminal. 

We are used to classical orbital mechanics, where the orbital velocity at any point is always smaller than the escape velocity from that point. Obviously this is not the case when dealing with black holes. 

[Green Baron]

To be precise, from my lay understanding: nothing with a rest mass can reach the limiting speed because its relativistic mass would become infinite (good old Lorentz-factor applies) and its impossible to accelerate an infinite mass. I am ignoring causality between reference frames here. (On the other hand, everything without a restmass has to travel at the limiting speed but that's not important here).

So, to develop @sevenperforce idea further, you can accelerate from an elliptical orbit to a hyperbolic and thus leave a body, or fly by on a hyberbolic orbit and use gravity for acceleration (or deceleration). That's Newton's mechanics modeled as conic sections.

But at the Schwarzschild radius Newton gives up and relativity takes over. A ship has to accelerate to the speed of light to hold position (which is impossible if it has restmass).

But relativity says: for the outside universe watching such a ship it stands still as it reaches the horizon and will never cross it (this answers part one of op's question, you cannot dip below in the reference frame of a distant observer). Passengers inside the ship will not be aware of the standstill, time outside just passes faster and faster until it literally runs out, and this should answer the second part, that there is no coming back from the event horizon.

 

Valid until a physicist overlooks this :-)

 

Edited March 26, 2017 by Green Baron
Took out the fantasy part ....

[0111narwhalz]

Would it be correct to say that a black hole is actually a shell at the event horizon, rather than a single point?

[Green Baron]

idk But the Schwarzschild radius is actually a radius. The sun's is 3km (or was that the diameter ?), mine is smaller :-)

It can't be observed directly because it does not reflect or radiate anything except maybe the hypothetical hawking radiation, but this is so faint that it can't be measured. Radiation of surrounding stuff is what deceives it, or jets from active galaxy cores, and indirect hints like movement of surrounding objects (Sagitarius A*). Stellar black holes are mostly incidents to find.

Edit: Another one is https://en.wikipedia.org/wiki/Cygnus_X-1. See mass and caclculated event horizon diameter. The "object" itself can be smaller than the horizon, if that answers your question.

I read that with the new generation of telescopes it might be possible to actually get an images of the effects of black holes, accretion disc, gravity lens, these sort of things. Interferometry - EHT laid/lais the foundations -, is the key to new insights. Onsights. Whatever.

Patience we must have :-)

 

Edited March 26, 2017 by Green Baron
Link to stellar black hole

[monophonic]

3 hours ago, Green Baron said:

But relativity says: for the outside universe watching such a ship it stands still as it reaches the horizon and will never cross it (this answers part one of op's question, you cannot dip below in the reference frame of a distant observer).

But the ship does not actually slow down to a standstill, right? It is just an artifact of light emitted/reflected from the ship needing exponentially increasing time to escape the vicinity of the black hole? All the way until that time becomes infinite at the event horizon.

[HebaruSan]

4 minutes ago, monophonic said:

But the ship does not actually slow down to a standstill, right? It is just an artifact of light emitted/reflected from the ship needing exponentially increasing time to escape the vicinity of the black hole? All the way until that time becomes infinite at the event horizon.

It depends whose frame of reference you're using. Gravitational time dilation is real. For the distant observer, time really does slow down for the ship near the black hole. From the perspective of the ship, nothing seems to slow down, but things further away from the black hole speed up. If the ship escapes and meets up with the distant observer, clocks carried by the two will show very different intervals elapsed.

[monophonic]

42 minutes ago, HebaruSan said:

It depends whose frame of reference you're using. Gravitational time dilation is real. For the distant observer, time really does slow down for the ship near the black hole. From the perspective of the ship, nothing seems to slow down, but things further away from the black hole speed up. If the ship escapes and meets up with the distant observer, clocks carried by the two will show very different intervals elapsed.

Give me a reference frame where matter does cross the event horizon please. I was wondering how the ship can seem to stop for ever - but as the light gets redshifted more and more as the ship nears the event horizon, is the EH the point where wavelength for those photons (as seen by the outside observer) becomes infinite? So as the ship seems to slow down it also seems to fade out of existence - or cool to absolute zero for emitted vs. reflected light?

[HebaruSan]

5 minutes ago, monophonic said:

Give me a reference frame where matter does cross the event horizon please. I was wondering how the ship can seem to stop for ever - but as the light gets redshifted more and more as the ship nears the event horizon, is the EH the point where wavelength for those photons (as seen by the outside observer) becomes infinite? So as the ship seems to slow down it also seems to fade out of existence - or cool to absolute zero for emitted vs. reflected light?

Ah, I specifically sidestepped the idea of a "standstill" at the event horizon, because I'm not sure that part is correct, if by that we mean that the ship's clocks approach a rate of zero seconds per our second. Wikipedia seems to agree with your interpretation, though, for what that's worth:

Quote

Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it. At the same time, all processes on this object slow down, from the view point of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift. Eventually, the falling object becomes so dim that it can no longer be seen.

 

[monophonic]

We seem to be at the limit of our combined knowledge then, @HebaruSan. Because that wikipedia article is my primary source (of confusion). 

Thank you for your time.

[Green Baron]

47 minutes ago, monophonic said:

Give me a reference frame where matter does cross the event horizon please.

The ship. It can cross it if not destroyed by gravitational forces or radiation of the accretion disc. In its reference frame it is not even aware that it has crossed an event horizon. But it cannot return. As it reaches the horizon time outside reaches infinity. Much has been speculated about what is inside but as far as i know physics cannot tell yet. Great unified quantum field bla theory is missing.

Btw. gravitational time dilation as well as that by speed (which is essentially the same) is as real as the mouse you are holding. It is responsible for the orbit changes of Mercury, it was measured by satellites, it must be taken into account by the GPS. It is not magic :-)

47 minutes ago, monophonic said:

I was wondering how the ship can seem to stop for ever - but as the light gets redshifted more and more as the ship nears the event horizon, is the EH the point where wavelength for those photons (as seen by the outside observer) becomes infinite? So as the ship seems to slow down it also seems to fade out of existence - or cool to absolute zero for emitted vs. reflected light?

Nobody can watch it because energy from the Schwarzschild radius does not go anywhere except towards the gravitational center. All lines lead inwards, sotosay. Yeah, what you say describes it pretty well i think.

I tried to avoid wikipedia except for the links i posted above. I have my half baked knowledge from cosmology books.

55 minutes ago, HebaruSan said:

Ah, I specifically sidestepped the idea of a "standstill" at the event horizon, because I'm not sure that part is correct, if by that we mean that the ship's clocks approach a rate of zero seconds per our second. Wikipedia seems to agree with your interpretation, though, for what that's worth:

 

Nope. The ships clock ticks just normal inside the ship. See above. The standstill is relative to an observer at rest (in the flat universe around). Physics doesn't say what happens at the event horizon, only short before. Just take a look at the formula on time dilation, when reaching speed of light it collapses into a 0 denominator, but just before it climbs very fast. In this wikipedia and my cosmology book agree that the ship stand s still at the event horizon relative to an observer in the flat universe. So, on the other hand, as that happens, the time of the universe has passed when the ship tries to cross the horizon.

Sounds logical to me ...

[HebaruSan]

2 minutes ago, Green Baron said:

Nope. The ships clock ticks just normal inside the ship. See above. The standstill is relative to an observer at rest (in the flat universe around). Physics doesn't say what happens at the event horizon, only short before. Just take a look at the formula on time dilation, when reaching speed of light it collapses into a 0 denominator, but just before it climbs very fast. In this wikipedia and my cosmology book agree that the ship stand s still at the event horizon relative to an observer in the flat universe. So, on the other hand, as that happens, the time of the universe has passed when the ship tries to cross the horizon.

Right, I got tired of typing "distant observer" and hoped that I could replace one of them with "our".

The potential problem here is that if Hawking radiation does exist, then "the time of the universe" is not correct because if you wait enough googol-to-the-googol years, the black hole will evaporate. So if the external observer sees the ship come to a stop outside the horizon, and then the black hole shrinks and eventually explodes with the ship still outside it, then we would like to reconcile that somehow with the ship's observation of its own passing the horizon with no problem. As far as I know, Hawking radiation is a pretty widely agreed upon phenomenon even though it hasn't been observed yet.

[HebaruSan]

Another thought experiment or two that might be relevant, or at least jumping off points for drawing finer distinctions.

We haven't stipulated any of the physical properties of the objects involved (mass, volume, charge, rotation, etc.) to come to the conclusion that the outside observer sees the ship come to a gravitationally-time-dilated halt above the event horizon, so that conclusion should apply to any object falling into any black hole.

Right off, this should mean that a black hole can never grow in the reference frame of an external observer, because from an external/distant frame of reference, any in-falling mass is frozen in time just above the event horizon, waiting for eternity to pass before it proceeds. Maybe this is the case, but every prior physicist's presentation on black holes that I've seen has implied otherwise, that in fact mass can fall into a black hole and that black holes can increase their mass over time this way in the reference frame of an external observer.

Further: What if instead of sending a ship, we send another black hole? The same conclusion should hold; from an external frame of reference, Black Hole #2 should slow down more and more and ultimately freeze before it passes through Black Hole #1's event horizon (and vice versa for BH1 passing through BH2's event horizon, of course). But the LIGO observations are generally agreed to be strong evidence that black hole mergers do in fact occur in our universe, in our frame of reference. So at the very least, event horizons can pass each other; whether we want to draw distinctions between them and truly physical objects is a more subtle question, but it makes me doubt that gravitational time dilation near the EH is so severe that time effectively cannot pass as observed from a distance.

Again, I don't consider these necessarily to be contradictions or reductiones ad absurdum, just apparent problems that may be real problems or may go away if the arguments are presented more carefully.

Edited March 27, 2017 by HebaruSan

[0111narwhalz]

If two black holes "collide," wouldn't their potential wells level out near their barycenter and thus create a sort of "tunnel" within which time is not dilated?

[Green Baron]

This can't be understood intuitively (foul excuse :-)). What can be measured from outside is the radiation from such events but this does not come from the Schwarzschild radius but from the area above, accretion disc and so on and this is clearly within the observable universe. The Schwarzschild radius is not, just until short above. So, in principle, the description of what happens at the event horizon is what mathematics imply. The "freeze" is not observable from outside because no information of it can escape (gravitational mass goes to infinite) and so probably your questions cannot be answered in our reference frame (time goes to division by 0).

See it like this: the object stops at the event horizon and does not pass though, instead, the event horizon expands (and that without hurting causality, wow :-)). Here is what i found about it.

Astrophysics can tell whether an object that is drawn towards a huge gravity well hits an event horizon (no signal) or a solid surface (energy burst on impact). When two black holes collide they are assumed to merge and form a single larger one.

 

To understand more of this experiments to research gravitational waves have been and are being built. Ligo and Virgo for example.

 

Edit: that Kevin Brown guy i linked above is somewhat of a mystery. Apparently he hasn't published more under that name, but was linked in the physics forum as well as in a university course so if you manage to wrap your brain around it then have fun :-)

Edited March 27, 2017 by Green Baron

[YNM]

10 hours ago, HebaruSan said:

Another thought experiment or two that might be relevant, or at least jumping off points for drawing finer distinctions.

We haven't stipulated any of the physical properties of the objects involved (mass, volume, charge, rotation, etc.) to come to the conclusion that the outside observer sees the ship come to a gravitationally-time-dilated halt above the event horizon, so that conclusion should apply to any object falling into any black hole.

Right off, this should mean that a black hole can never grow in the reference frame of an external observer, ...  ... Maybe this is the case, but every prior physicist's presentation on black holes that I've seen has implied otherwise, that in fact mass can fall into a black hole ...

.. What if instead of sending a ship, we send another black hole? The same conclusion should hold...

53 minutes ago, Green Baron said:

This can't be understood intuitively (foul excuse :-)). What can be measured from outside is the radiation from such events but this does not come from the Schwarzschild radius but from the area above, accretion disc and so on and this is clearly within the observable universe. The Schwarzschild radius is not, just until short above. So, in principle, the description of what happens at the event horizon is what mathematics imply. The "freeze" is not observable from outside because no information of it can escape (gravitational mass goes to infinite) and so probably your questions cannot be answered in our reference frame (time goes to division by 0).

See it like this: the object stops at the event horizon and does not pass though, instead, the event horizon expands (and that without hurting causality, wow :-)). Here is what i found about it.

Astrophysics can tell whether an object that is drawn towards a huge gravity well hits an event horizon (no signal) or a solid surface (energy burst on impact). When two black holes collide they are assumed to merge and form a single larger one.

One thing people often forget : gravitational redshift.

It is true that time dilation would come to an infinitely long timescales. But the redshifting will also be "infinite", leaving infinitesimally small wavelength. Those frozen objects are, therefore, practically invisible and unobservable. I suppose this is where Hawking radiation is supposed to come in - the idea that even if they still have to emit light or radiation (or, well, "equalizing entropy"), it will be obscure, indifferent from all the other things that has fell to the black hole (probably including the black hole itself).

10 hours ago, 0111narwhalz said:

If two black holes "collide," wouldn't their potential wells level out near their barycenter and thus create a sort of "tunnel" within which time is not dilated?

I don't think this is the case - they'll still be surrounded by curved spacetimes, if it (the "flat floor") ever exists. Guess that's where the gravitational wave comes from ? I don't know, someone who have these things in their academic line could go for it perhaps...

Edited March 27, 2017 by YNM

[sevenperforce]

When we talk about the black hole "growing", it's important to keep in mind that black holes are defined solely by their mass, their charge, and their angular momentum. This is known in physics as the no-hair theorem. No matter what went into the formation of a black hole, those are the only three observable things about it. From an outside perspective, two black holes are identical if they have the same mass, the same charge, and the same angular momentum.

So what happens when a black hole grows? Well, the only thing that CAN change is mass, charge, and angular momentum. The mass of the infalling object is added to the mass of the black hole. Recall that any object, no matter how small, has a gravitational field. Thus, when an object crosses the event horizon of a black hole, externally it is simply the merger of two gravitational fields. Since gravitational potential waves travel at the speed of light, it is a (relatively) simple matter to model their merger.

All that to say: talking about what "happens" to something falling into the event horizon is needlessly confused, because the object itself ceases to exist from an outside perspective; the only thing visible from afar is that the diameter of the event horizon increases ever so slightly.

An additional complication, which some here have touched on: the event horizon itself is defined by the location of the observer. We arbitrarily define the event horizon as viewed from infinity, but since all gravitational fields extend infinitely, every actual observer is observing from a different gravitational potential height. The event horizon observed by any particular observer will depend on how far they are from it; an observer relatively close to a black hole will observe an infalling object longer than an observer farther away. For the unfortunate individuals actually crossing the event horizon (assuming it is a large enough black hole that tidal forces do not shred them), they see the event horizon below them shrinking and shrinking while the spacetime behind them grows larger and larger without bound. 

Now, the no-hairs theorem, despite being strongly indicated by everything we know about black holes, suggests that information about the particles which fall into a black hole is destroyed. However, classical physics does not permit the destruction of information. Another problem is that all objects with non-zero temperature (including black holes, as shown by Bekenstein) must emit blackbody radiation as defined by Planck's law, but a black hole by definition cannot allow anything to escape. Hawking hypothesized the eponymous "Hawking radiation" as a solution to both the no-hairs problem and the blackbody problem: quantum tunneling at the event horizon permits some particles to escape to infinity, carrying radiation, information, and mass.

However, as is often the case with cutting-edge physics, each new solution poses a new problem. If the event horizon is entirely position-dependent and would not be visible to an infalling observer, how could it simultaneously be the source of a flood of particles? This is known as the firewall problem; Hawking radiation means the event horizon would literally be a "wall of fire" that would incinerate anybody crossing it.

Fortunately, quantum mechanics comes to the rescue here: quantum fluctuations in the gravitational field allow Hawking radiation to be emitted from any distance, solving the firewall problem.

Edited March 27, 2017 by sevenperforce

[sevenperforce]

5 hours ago, Green Baron said:

See it like this: the object stops at the event horizon and does not pass though, instead, the event horizon expands (and that without hurting causality, wow :-)). Here is what i found about it.

Causality is not "hurt" because the gravitational field of the infalling object already existed. We can model the merger of two gravitational fields without difficulty.

4 hours ago, YNM said:

Quote

If two black holes "collide," wouldn't their potential wells level out near their barycenter and thus create a sort of "tunnel" within which time is not dilated?

I don't think this is the case - they'll still be surrounded by curved spacetimes, if it (the "flat floor") ever exists. Guess that's where the gravitational wave comes from ? I don't know, someone who have these things in their academic line could go for it perhaps...

Time dilation is the consequence of a difference in gravitational potential, not a consequence of spacetime curvature. The gravitational potential saddle point between two black holes has no gravitational gradient -- you're not going to fall in either direction -- but it is still located at a lower gravitational potential than an outside observer, and thus time will run at a different rate.

Lots of confusing terminology here, as might be expected. The gravitational gradient, which produces acceleration toward mass, is the slope of the gravitational potential field, which is produced by mass.