Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: fish on 02/10/2012 13:39:39
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G'day,
I understand the premise of gravity distorting space time to a singularity. I understand that light cannot not escape the pull of a black hole once light is past the event horizon.
So.... Why would I be 'torn apart' if I went past the event horizon?
If I am trapped by the gravitation pull of earth from space, nothing happens to me till I impact the ground. If I was in a space ship near to Jupiter, once again the gravitational pull is not noticeable relative to me, til I meet with an opposing surface of the planet.
My question is - why would I be harmed be a black hole beyond the event horizon?
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The being torn apart bit is not something that happens at the event horizon. The EH is just the point from which, once passed, you could never escape. Being torn apart is the result of "tidal forces". These result from the difference in the gravitational field that is at the part of your body that is nearset the BH compared with that part that is furtheest away from the BH. The difference in the field results in you being stretched and, maybe, by quite a lot. You may well experience large tidal forces well before crossing the EH, though if the BH is large enough, you could cross the EH without noticing any ill effects at all.
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Would it depend on whether one approaches the black hole on a tangent vs directly plunging into the black hole?
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Would it depend on whether one approaches the black hole on a tangent vs directly plunging into the black hole?
As far as the tidal forces go, I don't think it makes any difference to a first order (i.e. you may well still be torn apart) though there may be some subtle higher order effects associated with the hard-to-solve mathematics resulting from a more complex trajectory.
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The problem with being torn apart is not the actual gravitational field but the gradient of the gravitational field this is because you are an extended body and as you approached the black hole the part of you that is nearer feels a stronger pull than the part that is furthest away.
For a typical stellar mass black hole say around 10 solar masses with a radius of 30km this is about ten million earth gravities per meter which would tear you apart very violently. This gets less as the black hole gets bigger.
For an intermediate sized black hole with about 30,000 solar masses with an event horizon about as big as the planet jupiter the gravity gradient is about 1earth gravity so it would feel a bit like you are hanging by your arms from a bar and just survivable
For a really big black hole like the ones at the centre of big elliptical galaxies with about 10 billion solar masses and about the size of our solar system the gradient is totally unnoticeable.
The reference for these figures is http://xaonon.dyndns.org/hawking/ which allows you to calculate what any sized black hole is like.
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So, does the Rocche limit (http://en.wikipedia.org/wiki/Roche_limit) apply equally independent of the trajectory, direct inward vs tangential?
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the trajectory is not critical because they are very different cases. Let me explain
Firstly the Rocche limit deals with the gravitational gradient of a star or planet breaking up a satellite of a particular size and rigidity as it orbits it would normally apply to approximately tangential motion.
The breakup of any object due to gravity gradient will depend on several things, notably the gravitational gradient the strength of the object, the size of the object and also the time during which it is subjected to the disrupting forces.
An object in a stable orbit making a close approach ail experience plenty of time and repeated stresses so even the slightest breakup wil have time to show
An object falling directly towards the gravity source the forces will increase continually until the collision this will take less time so an object may start to disrupt at one point but the forces will increase quickly to cause greater disruption but the time this takes may not allow the initial disruption to be observed.
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The conventional theory with black holes is that you can fall past the event horizon unharmed, provided the black hole is big enough.
However, there is also a recent theory that says you can't fall past the event horizon:
http://en.wikipedia.org/wiki/Gravastar
Basically, IIUC the authors of the theory think there's a sort of shock wave of Hawking-like radiation at the event horizon that tears things apart.
But the theory isn't generally accepted at the moment.
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The Roche Limit defines the orbital radius where the gravity of the central body is stronger than the self-gravity of surrounding dust. This stops the dust from coalescing to form an orbiting planet or moon.
However, an already-solid body can orbit slightly within the Roche Limit, because it's solid surface holds it together more strongly than loose dust. http://en.wikipedia.org/wiki/Roche_limit#Explanation
Approaching a black hole in a spaceship (or spacesuit) makes you more intact that loose dust. When free-falling near a smallish black hole, the acceleration of your feet will exceed the acceleration of your center of gravity, which will exceed the acceleration of your head, causing an effect similar to being on the rack. The scientific word for this is "Spaghettification": http://en.wikipedia.org/wiki/Spaghettification
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But it also depends on the conditions you meet past that event horizon, in some solutions I understand that there is a possibility for you not to get 'spagettified'. And it also have to do with what definition you locally will find of a 'space' as you're inside, maybe I can find some description of that on the net?
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Here is one nice.
"Black holes can be low density.
Of all the weirdnesses about black holes, this one is the weirdest to me.
As you might expect, the event horizon of a black hole gets bigger as the mass gets bigger. That’s because if you add mass, the gravity gets stronger, which means the event horizon will grow. If you do the math carefully, you find that the event horizon grows linearly with the mass. In other words, if you double the black hole’s mass, the event horizon radius doubles as well.
That’s weird! Why?
The volume of a sphere depends on the cube of the radius (think way back to high school: volume = 4/3 x π x radius3). Double the radius, and the volume goes up by 2 x 2 x 2 = 8 times. Make the radius of a sphere 10 times bigger and the volume goes up by a factor of 10 x 10 x 10 = 1000.
So volume goes up really quickly as you increase the size of a sphere.
Now imagine you have two spheres of clay that are the same size. Lump them together. Is the resulting sphere twice as big? No! You’ve doubled the mass, but the radius only increases a little bit. Because volume goes as radius cubed, to double the radius of your final clay ball, you’d need to lump together eight of them.
But that’s different than a black hole. Double the mass, double the size of the event horizon. That has an odd implication…
Density is how much mass is packed into a given volume. Keep the size the same and add mass, and the density goes up. Increase the volume, but keep the mass the same, and the density goes down. Got it?
So now let’s look at the average density of matter inside the event horizon of the black hole. If I take two identical black holes and collide them, the event horizon size doubles, and the mass doubles too. But volume has gone up by eight times! So the density actually decreases, and is 1/4 what I started with (twice the mass and eight times the volume gives you 1/4 the density). Keep doing that, and the density decreases.
A regular black hole — that is, one with three times the Sun’s mass — with have an event horizon radius of about 9 km. That means it has a huge density, about two quadrillion grams per cubic cm (2 x 1015). But double the mass, and the density drops by a factor of four. Put in 10 times the mass and the density drops by a factor of 100. A billion solar mass black hole (big, but we see them this big in galaxy centers) would drop that density by a factor of 1 x 1018. That would give it a density of roughly 1/1000 of a gram per cc… and that’s the density of air!
A billion solar mass black hole would have an event horizon 3 billion km in radius — roughly the distance of Neptune to the Sun. See where I’m going here? If you were to rope off the solar system out past Neptune, enclose it in a giant sphere, and fill it with air, it would be a black hole!
That, to me, is by far the oddest thing about black holes. Sure, they warp space, distort time, play with our sense of what’s real and isn’t… but when they touch on the everyday and screw with that, well, that’s what gets me.
I first thought of this at a black hole conference at Stanford a few years back. I was walking with noted black hole expert Roger Blandford when it hit me. I did a quick mental calculation to make sure I had the numbers right, and related to Roger that a solar system full of air would be a black hole. He thought about it for a moment and said, "Yes, that sounds about right."
And that, me droogs, was one of the coolest moments of my hole life. But thinking about it still makes my brain hurt."
From Ten things you don’t know about black holes. (http://blogs.discovermagazine.com/badastronomy/2008/10/30/ten-things-you-dont-know-about-black-holes/)
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But there is one point more to it, it also have to do with the 'space' existing inside and there I couldn't find anything specific about it, but I know I wrote about that in New Theories, if you're interested? And also very, and I do mean very, patiently looking for it :)
And that view has to do with 'frames of reference' being observer dependent, as I've come to think about it.
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As for the definition of 'space' moving faster than light I don't agree. 'Space' is strange and it can be distorted, the distortion can 'move' as defined by us, possibly? And as it is the universe itself, it's clearly outside our definitions of what limits we have inside it. But I don't think of it as a 'motion' in itself.. It's just what it is defined as, a 'distortion'. And that's a crucial difference if you imagine a 'warp drive'. But it's tricky, and I'm not sure.
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Hmm, looking for another link I found this though :) It's a older version but read it carefully.
"Black Holes
So what happens when the distortion becomes really massive? One idea is that we get a black hole. First I will cover the general idea of a black hole, then discuss some of the issues involved.
In the collapse of a star more than 15 times the size of our sun, the theory is that the gravitational collapse cannot ever stop. First the atoms collapse to nuclear size, then the nuclei themselves collapse without limit under the extreme gravity, compressing the star to a point. Unlike neutron stars there may be no explosion that blasts part of the star out into space after the initial collapse - the collapse is one-way only, especially if the angular momentum is low.
Take two observers - ‘A’ who stays far from the black hole and ‘B’ who travels from ‘A’’s position into the black hole; both carry clocks that the other can see.
As ‘B’ leaves ‘A’ he travels in free-fall towards the black hole. As he does so ‘A’ perceives ’B’’s clock to be slowing down drastically, and his rate of acceleration into the block hole seems to be less than it should be. For ‘B’, however, his time is unaffected and he falls as he would expect. This time dilation increases as ‘B’ gets closer to the black hole.
Behind him ‘B’ sees a picture of the universe behind him that distorts more and more as he falls. At first he sees simply what is behind him, but the gravitational lensing causes him to see more and more of the universe round the black hole until at a radius 3.G.M/c2 the whole of the universe around the black hole is visible behind him (where G is the gravitational constant and M is the mass of the black hole). This is the photon sphere, where photons can orbit around the black hole. Beyond this point the view behind him closes up into a cone surrounded by light that has come up from below him and been lensed back down. The view is similar to that of an underwater swimmer looking up at the surface - he sees a cone that compresses everything visible above the surface, surrounded by reflections of what is under the water.
He continues until at a certain point the time dilation as seen by ‘A’ becomes infinite. At this point ‘A’ sees that ‘B’ has stopped dead - he hangs forever at this point, stuck in frozen time till the end of the universe. ‘B’’s perception is that he is still accelerating into the black hole and there is nothing abnormal about his fall.
This point, where ‘B’’s time is infinitely dilated, is an event horizon termed the Schwartzchild radius. It exists at this point only for a remote observer such as ‘A’. As you approach the black hole the event horizon moves ahead of you, so that for ‘B’ there is a different event horizon ahead of him, where someone further into the black hole than he will experience infinite time dilation relative to ‘B’’s time - or the “square of infinite” time dilation relative to ‘A’’s time. There is however only one Schwartzchild radius - the outermost event horizon - and this occurs at 2.G.M/c2. For a star with just two solar masses left after collapse the Schwartzchild radius is about 6km and the photon sphere radius is about 9km.
Let us continue ‘B’’s journey to the centre of the black hole. He falls normally, according to his own perception, even though with respect to the outside world of ‘A’ he ultimately has many powers of infinity of time dilation. Finally reaching the centre the gravitational field is so high that nothing stops the collapse into a single point, and ‘B’ is swept into it. At this point the mass density reaches infinity, causing the gravitational field equations to have a mathematical singularity at this point - that is, they have no solution. So the laws of space and time do not apply.
As ‘B’ falls into the black hole his mass and charge are simply added to the black hole. Mass and charge are simply added to the black hole. So if the sun suddenly collapsed into a black hole the gravitational field at Earth’s orbit would be unaffected and Earth would continue in its normal orbit without perturbation.
Anything wrong with this picture? Well, there have been a great deal of massive stars in the lifetime of the universe, and so far we have not detected one despite looking hard. We should see them by radiation from infalling cosmic gas and dust. So maybe black holes do not exist.
What arguments are there against the existence of black holes? The first and most obvious is that spatial dilation has not been allowed for in the above argument, and it thereby violates energy conservation laws. Let us review the above fall of ‘B’ into the region of the black hole.
As ‘B’ falls into the black hole ‘A’ perceives that he shrinks in size. ‘B’ on the other hand sees ‘A’ grow in size together with the outer universe. As ‘B’ free-falls into the gravitational field he exchanges mass for kinetic energy, so that at the Schwartzchild radius, where spatial dilation is infinite, he has become of negligible size and virtually all his mass has been exchanged for kinetic energy. ‘A’ perceives him to have zero mass and his kinetic energy is m0.c2, where ‘m0’ was his starting mass in the greater universe, so his ratio of kinetic energy to mass is infinite. ‘B’ perceives himself to have the same mass as he started with, but he has picked up an infinite kinetic energy, so again his ratio of kinetic energy to mass is infinite. With this ratio he can travel at only one speed - light speed. He travels with the photons across the Schwartzchild radius.
His kinetic energy does not contribute to the gravitational field, since that is reference-frame dependent. Only his mass can. As far as ‘A’ is concerned he contributes zero mass to the black hole. By extension, nothing inside the Schwartzchild radius can contribute any mass or charge to the black hole - all its energy is kinetic - and hence the event horizon cannot form - it is self-limiting by the spatial dilation. Hence there is no singularity.
Another factor that affects the formation of the singularity is that at the putative event horizon ‘B’ is infinitely dilated, but the event horizon is finite. Hence ‘B’ perceives that the space he is entering has expanded dramatically - black holes are infinite on the inside. At the event horizon he perceives the radius to have become infinite, although in reality it is he whose size has become negligible.
Truly massive stars may therefore collapse like neutron stars, with the piledriving pulse of the collapse converting mass into kinetic energy in a violently-dilated space. The resulting rebound explosion blasts all but a small remnant out into space. The gravitational field turns much of the remnant’s mass into kinetic energy which fuels the explosion, and so is lost to the star forever. And so it can be seen that massive suns create energy in the following sequence:-
Fuse hydrogen into helium - 0.72% efficient
Fuse helium and hydrogen into heavier elements up to iron - 0.2% efficient
Convert mass into kinetic energy in gravitational collapse - 5.0 % or more
For massive suns the last is the most efficient, give by far the highest ratio of energy output to total mass involved. Since the collapse is so fast, taking less than a second, the resulting release of energy is incredible. This energy output is greater than all the energy produced in the previous life of the star.
There are other arguments against singularities:-
Relativity Theory uses the simplifying assumption that all masses are points. Since a point mass is itself a singularity the black-hole singularity is inevitable. But Quantum Theory shows that the position of a particle is associated with a probability distribution. Clearly if the position of a particle is indeterminate the singularity cannot form since it requires a point of zero dimensions with no indeterminacy. “Quantum Relativity” attempts to address this issue. An associated argument is that for the same reason a particle’s positional probability distribution can lie across the event horizon and so a black hole will slowly “leak” particles and thereby evaporate. The counter argument is that if a black hole can form the particle becomes embedded in an infinite space inside an event horizon, and its probability distribution cannot extend beyond infinity.
The time taken to form the singularity (again according to ‘A’) would be infinity to a high power so cannot happen in a real limited universe. We could of course take the role of ‘B’ or some deeper observer to make it more possible, but that would be in a purely theoretical daughter universe that is forever closed to us by infinite time."
As for what is the real 'reality' in such a description? it all depends on where you stand, as I see it?
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from Extreme Gravity (http://www.mariner.connectfree.co.uk/Gravity/Extreme_gravity/extreme_gravity.html) And this is about a non rotating black hole I better add.