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Apparently it is theoretically possible for a planet to achieve a stable orbit around the singularity at the centre of a black hole within the event horizon. This means that life could hypothetically form inside a (presumably supermassive) black hole.

There are obviously many problems with this, but I suggest we ignore those for a while.

What I'm interested in is how quickly (or slowly) time would pass for this planet taking into account time dilation due to extreme gravity and how much time this leaves for life to develop before this black hole explodes due to Hawking radiation.

Any other unavoidable events that will eliminate all possibilities of life inside this black hole along with when they will take place would also be interesting.

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    $\begingroup$ How quick or slow in relation to what? I suspect you mean in relation to Earth, but better ask than guess wrongly ^^. $\endgroup$ – Layna Feb 12 '15 at 14:52
  • $\begingroup$ @Lanya yeah, earth is fine. Most frames of reference experience time at very similar rates anyways. $\endgroup$ – overactor Feb 12 '15 at 14:57
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    $\begingroup$ No object can achieve stable orbit inside of the event horizon. A different definition for the event horizon is the lowest altitude above the singularity that light can achieve a stable orbit. Light, moving at the speed of light cannot orbit a singularity beyond the event horizon. $\endgroup$ – Nick2253 Feb 12 '15 at 15:15
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    $\begingroup$ Actually, the radius at which light orbits a black hole is 1.5 times the radius of the event horizon, for a non-rotating black hole. $\endgroup$ – 2012rcampion Feb 12 '15 at 15:17
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    $\begingroup$ Fair warning: whenever I see "how could life develop in X" questions, my immediate response is "define 'life.'" That word actually doesn't have an agreed upon definition, as surprising as that might sound. $\endgroup$ – Cort Ammon Feb 12 '15 at 15:34
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Original answer, preserved for posterity

Here's the paper.

First, there are some important assumptions that the author - Vyacheslav Dokuchaev - made. Specifically, there are two scenarios:

  1. The particles are charged and the black hole is not rotating. This is not helpful, because all the particles in a given object would have to be charged perfectly. This is not going to happen in an object even as small as a human.

  2. The particles are uncharged and the black hole is rotating. Rotating black holes, described by the Kerr metric, can easily exist, and there's nothing that says that one body can't orbit a Kerr black hole.

So one (or both) of these scenarios must be satisfied.

Second, Dokuchaev mentions life only once outside the introduction, conservatively saying

We hypothesize that civilizations of the third type (according to Kardashev scale [28]) may live safely inside the supermassive BHs in the galactic nuclei being invisible from the outside.

He alludes to life several other times throughout the paper, but barely touches on it. Discovery has really exaggerated the paper's implications: Dokuchaev really has only shown that particles can orbit inside the event horizon in certain conditions. And that's if the paper is entirely correct.

The Discovery article mentions the evaluation of one other scientist, Dr. David Floyd. Floyd says that the paper raises interesting questions, but it also raises some problems;

Astronomer Dr David Floyd from the Australian Astronomical Observatory and the University of Melbourne says even if the theory is correct, it would be impossible to know what is occurring beyond the event horizon of a black hole.

"At this point — and perhaps forever — we're restricted to making untestable assertions," says Floyd.

"As far as we know, matter would go into free fall, that is, it would all fall into this tiny infinitesimal point at the centre which forms the singularity."

Floyd says that one shortcoming of the paper is that it assumes radiation has no impact on orbits inside the black hole.

"It wouldn't take much to produce drag which would slow down the orbits described in Dokuchaev's paper, causing them to collapse onto the singularity".

And that's just talking about particles orbiting inside the black hole - not taking life into account!

I don't think the paper gives a convincing argument at all.

What I'm interested in is how quickly (or slowly) time would pass for this planet taking into account time dilation due to extreme gravity and how much time this leaves for life to develop before this black hole explodes due to Hawking radiation.

We can't use a simple approximation that would be used around Schwarzschild black holes, so we have to go to the Kerr metric. The formula for that is way too complicated to work with.

Another problem with using time dilation inside the black hole is that you end up with a factor of $$\sqrt{-a}$$ where $a$ is less than 1. So we have a bit of a formula breakdown for non-rotating black holes. This may be the same for rotating black holes - impossible to calculate.

For the time it takes for black holes to evaporate, I got $$4.63 \times 10^{104} \text{ seconds}$$ So they'll have a loooong time. Wikipedia gives a much larger figure, though the mass of the black hole is different.

I really don't think that life could live here, though.


New answer

That's the original answer. I want to rework it, because I was in a bit of a rush when I wrote it, and it could be better. So I'll mostly scrap that and start anew. I'll reuse some bits, though.

Correct me if I'm wrong, but here's the setup:

  1. The setting is a supermassive black hole, like the one at the center of our Milky Way, Sagittarius A*.
  2. There is some sort of planet or other body orbiting inside the event horizon.
  3. This body can presumably support life, illuminated by the surrounding radiation.

You want to know:

  1. The time dilation the planet would experience.
  2. Whether or not life could develop before the black hole evaporates due to hawking radiation.
  3. What could happen to jeopardize that life.

Time dilation

For a non-rotating (i.e. Schwarzschild) black hole, the formula for time dilation is $$t+0=t_f \sqrt{1-\frac{2GM}{rc^2}}=t_f \sqrt{1-\frac{r_0}{r}}$$ The issue for using this for an object within the event horizon is that the term $$\frac{r_0}{r}>1$$ and so we get an imaginary number.

For a rotating black hole, the equation is more complex, as shown here: $$\frac{dt}{d \tau}= \frac{1}{\Delta} \left[\left(r^2+a^2+\frac{2Ma^2}{r} \right) e - \frac{2Ma}{r}l\right]$$ where $a = J/M$, $\Delta = r^2-2Mr+a^2$ and $e$ and $l$ are constants. The calculations would take a while and depend quite a lot on the properties of the black hole. If we know $M$ - which we do - and we know the black hole's angular velocity, $\omega$, we should be able to figure it out. That would take a long time, though. Feel free to plug in some numbers and figure out how long you've got.

This and this are also helpful.

Hawking radiation

There are a couple relevant formulas for Hawking radiation: the temperature of the black hole: $$T=\frac{\hbar c^3}{8 \pi G M k_B} \approx \frac{1.227 \times 10^{23} \text{ K}}{M} \text{K}$$ the temperature of the emitted Hawking radiation: $$T_H=\frac{\hbar c^3}{8 \pi G M k_B}=T$$ the power emitted by the black hole: $$P=\frac{\hbar c^6}{15360 \pi G^2 M^2}$$ and the time it will take for the black hole to evaporate: $$t=\frac{5120 \pi G^2 M_0^2}{\hbar c^4}$$ Doing the calculations shows that the temperature of the Hawking radiation is negligible, as is the power emitted. The time is on the order of $10^{100}$ years, perhaps a few magnitudes higher. That's for the outside world; the people inside will experience less time than that. If you could calculate that. . .

But all is not lost! Black holes - and especially supermassive black holes - generally have accretion disks surrounding them containing hot gas, dust and plasma. As I explained here, the formula for the temperature of the accretion disk is $$T(R)=\left[\frac{3GM \dot{M}}{8 \pi \sigma R^3} \left(1-\sqrt{\frac{R_{\text{inner}}}{R}} \right) \right]^{\frac{1}{4}}$$ This will give you more energy than the Hawking radiation, and it will prolong the life of the black hole. Supermassive black holes are monsters; they can eat stars and gas clouds. It throws a wrench into your calculations, but it gives you hope for the life.

Things that could destroy life

It also fits into the category of "Any other unavoidable events that will eliminate all possibilities of life." In fact, all of the things in this category have to do with the black hole eating up something or merging with another black hole. The conditions here would be extreme - even more incredible gravitational forces, incredible temperatures, strong magnetic and electric fields. . . The one thing that could destroy this life would be an unfortunate encounter with matter coming into the black hole.

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  • $\begingroup$ This is a nice breakdown of the actual article, but it doesn't directly answer my question. You do make a good point for life inside a black hole being incredibly unlikely though. $\endgroup$ – overactor Feb 12 '15 at 17:11
  • $\begingroup$ @overactor Apologies, I had to go after I wrote it. I'll touch it up and improve it. $\endgroup$ – HDE 226868 Feb 12 '15 at 19:59
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    $\begingroup$ If time-dilation is an imaginary number, it means you need to work in a new reference frame. $\endgroup$ – PyRulez Jul 28 '15 at 15:14
  • $\begingroup$ I'm curious: Why are you using the Schwarzschild metric for time dilation inside the hole, when as you said, to be able to have anything orbiting in there inside at all, a different metric must be in play? $\endgroup$ – The_Sympathizer Sep 11 '15 at 7:12
  • $\begingroup$ @mike3 I showed the calculations for the Schwarzschild metric as an example, because it is commonly used, as it is the simplest solution (the Ker metric is not quite as common). Besides its simplicity, I used it because we're concerned with the effects of the black hole on the planet, and so we can approximate the planet as a massless test particle in the black hole's gravitational field. $\endgroup$ – HDE 226868 Sep 12 '15 at 21:02
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When you start asking about time dilation the important question is "Relative to what?" You don't say so I'm going to make some reasonable assumptions like "A planet well outside the event horizon but not vastly far away or moving vastly fast." In the same galaxy say.

Likewise if we assume some basic commonsense assumptions about time, space and causality that I think your operating under, namely because everyone does, the answer to amount of time dilation the planet would experience is:

"More than infinity."

The more than infinity answer is the reason we have an event horizon in the first place. How long do you have to wait for light to escape from beneath the event horizon? More than an infinite period of time. IE it never will.

Note that this doesn't apply to other objects inside the event horizon, near to the planet in question. They could still pass signals to each other so the sense of time passing that would make things like time dilation be sensible, as long as you restrict your question to "Close-by".

The event horizon isn't like some sort of magical brick wall, a barrier where assumptions like "There is space, time and stuff on the other side" still hold true.

Its the point where your fundamental commonsense notions of time, space, objectivity and relationship totally break down.

Whats totally weird about it is where your standing matters. Outside the black hole the answer to the question

"Whats going on inside the blackhole"

the answer is

The question is meaningless. Their is no possible relationship you can have with anything past the event horizon.

And so you can never see anything "fall" past the event horizon. Time dilation will slow it down and down, the stream of photons from that object becoming a trickle and then on to a vastly rare occurrence until the black hole itself dissolves in a blast of hawking radiation. But even if the black hole didn't dissolve you could wait an infinite period of time and never see the object cross the horizon.

But if your the observer falling into the blackhole their is no event horizon. You go straight past the point that the rest of the observable universe says isn't there. You can relate to stuff that fell in with you. Their is a sense that their is an inside the blackhole. But "outside" the blackhole starts to vanish. Red-shifted away to nothing.

But as I said, this is in terms of "commonsense" notions of time and space. No one said you had to stick with those notions and people who study this stuff have come up with non-commonsense ways of describing it.

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It cannot. Distribution of matter inside the black hole is symmetric agains the BH center (as if all its mass were in the center or along the surface). So there cannot be any structure inside. Otherwise it would be possible to transfer information from inside BH to the outside by moving mass bodies inside.

Apparently it is theoretically possible for a planet to achieve a stable orbit around the singularity at the centre of a black hole within the event horizon.

No, even mathematically it is impossible. Not even close enough to the BH outside it. Inside ergosphere (which is outside the BH surface) the centrifufgal force is directed towards the BH center. So the faster you revolve around the BH the faster you fall. So any body orbiting BH will fall faster than a directly free falling body.

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  • $\begingroup$ It depends on the perspective of the observer. The perspective from inside the black hole is completely different from outside the black hole. Apples and oranges. $\endgroup$ – Serban Tanasa Feb 28 '15 at 2:40
  • $\begingroup$ @Serban Tanasa there is no perspective from inside as I already mentioned. $\endgroup$ – Anixx Feb 28 '15 at 9:27
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Going towards a black hole will eventually cause the direction towards the singularity to flip and become a timelike dimension. Since nobody has any clue as to the conversion ratio between space and time, it is unclear how much time an object inside a black hole has. Either way, attempting to imagine the inside of the black hole as if it were normal space is a mistake.

Past the even horizon, no matter what you do, you will move towards the singularity. This is because past the event horizon it takes a speed higher than the speed of light in a vacuum to move outwards, so moving outwards becomes impossible. This makes the forward direction time-like.

Probably, you could move up and down in what used to be the time-like dimension, so each spherical cut we can imagine making through a black hole event horizon is a slice through a multitude of time-like paths, rather than a time-like instant as it would be in normal space. Now if you ask me how that makese sense since black holes have a definite origin point in our spacetime perspective and will likely undergo Hawking radiation death in the impossibly distant future, I haven't a clue...

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Ok, this does not include exact maths... for that, I leave you to physicists.

First: Hawking Radiation would apparently not affect your black hole... it only matters for very small ones:

This surprising new insight showed that there is still much to learn about black holes. However, Hawking's glow is completely irrelevant for any of the black holes known to exist in the Universe. For them, the temperature of the glow is almost zero and the energy loss is negligible. The time needed for the black holes to lose much of their mass is unimaginably long. However, if much smaller black holes ever existed in the Universe, then Hawking's findings would have been catastrophic. A black hole as massive as a cruise ship would disappear in a bright flash in less than a second.

Source

Shortened because I did mess up the direction....

Space Travel would give them some serious challenges: send a ship closer to the black hole, or farther away from it, they would get into detectable time dilation differences very quickly... any manned mission would have to take that into account.

It DOES provide them with neat possibilities for science, though. Need to do your calculations very quickly? Put up an automatic satellite to do computations further away from your friendly black hole.

I am not 100% sure of how observability of far away objects works with time dilation, but sending something IN so you can watch thinks on it happen more slowly than they usually would sounds like a feasible scheme.

Also, you could send out objects (or even people) you want to preserve further in... and bring them back when you want them, still relatively "fresh".

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    $\begingroup$ Objects in a massive gravitation field would experience time dilation, not time acceleration, so the black hole civilization would age significantly slower than we do, and would therefore develop much slower than we do. $\endgroup$ – Nick2253 Feb 12 '15 at 15:27
  • $\begingroup$ @nick2253 yes, however from their point of view a satellite moving away from the centre would process faster... $\endgroup$ – Tim B Feb 12 '15 at 19:01
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Life might develop inside (at least some) black holes without limitation.

We know (and apparently can know) nothing about the internal structure of black holes in general. They're a mathematical construct we came up with to account for the fact that we can't imagine anything preserving the structure of a dying star once it's massive and degenerated enough to fuse its neutrons. All we know about the inside from the math is literally nothing.

However, if you look into the debate surrounding the cosmological constant and the "shape" of the universe (open, flat, or closed), you will find that working scientists seem to believe that we live in a universe that is very near the boundary of "flatness", i.e. a universe with a maximum degree of expansion beyond which it will never expand. Flat and closed accounts of our universe look very much like black holes in the following sense: the Schwarzchild radius (the radius into which you'd have to pack all of the mass to make a black hole of it, 2GM/c^2) of the universe comes out equal to or larger than the radius of the observable universe. That means that if these cosmologists (those proposing flat and closed universe theories) are right, we currently live inside a black hole. Hence, it's absurd to suppose that being inside a black hole places some limitations on the development of life which we haven't considered.

One important caveat: surely you've heard of dark matter and energy. Well, for our universe to be flat or closed it has to be made of MOSTLY dark matter and energy. So, if the dark energy stories turn out to be bullshit, we will discover ourselves in an open universe with no idea what the interiors of black holes are like.

Your sub-questions about the time dilation within the black hole seem meaningless to me, there's simply no access to the outside of the black hole to allow for a comparison between interior and exterior frames of reference.

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Here's a fun link (warning, it's old): (http://jila.colorado.edu/~ajsh/insidebh/schw.html) that shows what it's like to fall into a black hole. The video is short and has some artificial inlays to help you understand what's going on and it does explain the frame by frame what's happening.

Basically, the premise is flaw because once inside the event horizen, you are now falling towards the singularity at a speed nearing the speed of light. Space is so warped by the gravity at this point that any object is now falling at an infinetly increasing near light speed (if you do get up to light speed, you can get out... if you haven't fallent too far... you just get faster and faster and approach it). You also have matter undergo speghettifacation, which is a lengthening and thinning of the object as it falls.

Now, the link does helpfully show the points where you can keep an orbit. At 1.5 times the event horizen radius, orbit is possible with a degree of assistence and photons can maintain a stable orbit, essentually creating a weird effect where our perception of the stuff behind the black hole is warped around it.

At 3+ times the Event Horizen Radius, an orbit is stable.

Your confusion comes from the fact that Supermassive Black Holes a surpringly low average density in the volume of space inside the Event Horizen. The largest known black hole has a mass of 21 billion times that of our sun and an event horizen with a radius of 63 billion kilometers. Since the bulk of all that matter is contained in the singularity, there really isn't anything between the point of no return and the singularity to get in your way.

For comparison, if our sun was to collapse into a black hole (it can't, too small) it would have an event horizen with a radius of 3 km. While Earth would be doomed, it would be from the lack of and heat provided by the sun, not the black hole. In fact, the mass of the sun hasn't gone anywhere and we would Earth and all the other planets et. al. would maintain their orbits. It's important to note we were never inside the event horizen to begin with.

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Until the interior of the black hole experiences heat death.

That time entirely depends on the size of the black hole, which has (as far as I'm aware) no theoretical limit - you can make it as big as you want, which means you can stick an entire galaxy or galaxy cluster inside of it to support your lifeforms, slowly spiraling inwards.

Edit: removed the "our universe" reference as the article wasn't quite what I was originally thinking.

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