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Hey!

I've had some thoughts about black holes for a while, and I am confused about the singularity.

A singularity is a word that is often mentioned when it comes to black holes, but why do people think that black holes contain a singularity really?

I mean, wouldn't it be enough to have an object with a ratio between mass and size making the escape velocity faster than the speed light to create a black hole?

Why does the radius have to be zero?

Lets say earth had a mass of billions of suns, wouldnt it be considered as a black hole even tough the radius isn't zero?

// Andreas

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It contains a singularity, because there is no known force to oppose gravity on the scale of these masses.

Below 1.5 solar masses (approx) the electron degeneracy pressure can resist gravity, making a stable system.

After that and below 3ish solar masses, the atoms themselves are crushed into neutrons, and that maintains a pressure outwards to counteract gravity (a neutron star). Past this point (with possible exception of quark stars), there is nothing left to resist the gravitational pressure, so it collapses in on itself to a singularity.

That said - no one really knows what goes on in a black hole, as no information can escape (probably!).

Anything with a radius/mass ratio < 2G/c2 will make a black hole. So to make one you either have to squash the radius of the object, or increase the mass (without changing the radius) - or both. For most black holes, it's the radius that decreases whilst the mass stays the same.

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The problem is in getting sufficient density to create a body with an escape velocity greater than the speed of light.

Neutron stars are just about as dense as an object can get before the subatomic particles "collapse". Keep throwing mass at a neutron star and it will reach the point at which the subatomic particles collapse. Then it ceases to have physical structure, it's just pure mass. Nothing remains to stop it collapsing into a single point - the singularity.

At the other end of the spectrum, there is the concept that our universe is massive enough to be effectively inescapable to light but has no singularity. It isn't collapsing because it's still expanding after the big bang. But what next? The big squeeze??

We live in a black hole?? :)

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I recall a paper on black holes from many years back it was not aimed at the pure maths of things but I do recall the bit that said that a mountain on the surface of a black hole body would be a high as 2 or even 3 molecules in height. So at that stage the idea was that a black hole body was a finite size and not a singularity.

Suppose it depends on what a singularity is defined as and whether or not the term has just become associated with black holes by common use. We cannot see inside one so what is down there is purely theoretical, and the one thing about theory is it can be massaged to what you want. If you want to show there is a non-zero size you select the conditions/theorems to indicate that result, if you want to show zero size you select the conditions/theorems to indicate that result.

We do not know if the bit at the bottom has a size or not, in some ways it might be convenient to assume a zero size, in others more convenient to assume a non-zero size. A zero size could mean that any equation that uses the size can be ignored, equally dividing by zero is problem area.

Very nice to have a zero size and say that by assuming a zero size or singularity then the equation simplifies to ??? and so the theory that the moon is made of green cheese is proven. Otherwise it could be an Emmental cvheese with lots of holes in it.

The problem with making the assumption that there is a finite sized lump at the bottom is someone will ask "What size is it?" If you say a zero sized singularity that blocks that question.

I tend to think more along the lines of a finite sized lump, for the following:

If it'sa singularity then the density will be infinite, the size will be zero, so somehow we get that InfinityxZero, 2 somewhat unwanted values in maths, gives a defined values such as the mass.

Have no problems if it is zero but means that the previous bit needs limitations applied and a few other bits, the above is similar to how I see simple integration working, and that isn't a problem.

So pick whichever one you want and let whoever else pick the one they want, then don't argue.

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We don't know what really happens inside a black hole. The singularity is the point where the equations of general relativity break down, some terms becoming infinite. Singularities are mathematical concepts which may bear no relation to physical reality. The same problem has occurred in other branches of physics, and is typically an indication that the theory is incomplete. It is thought that a theory of quantum gravity would not feature any singularities. There are many competing theories, but they are very difficult to test, as the effects of quantum gravity are extremely weak.

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A nice sum up :). It is very easy to read a lot into the meaning of singularity in words, and whatever philosophy ands thoughts/consequences that may be derived form it, but mathematically it is quite easy to understand.

In general as Knight of Clear Skies says, the best you can only really say that the point at which a singularity occurs the result is undefined. There may be ways of rewriting the problem to get rid of the singularity, but till then, you are stuck with it and the consequences of mathematical rules that come with it.

A sort of easy way to appreciate the idea of a singularity is that it is just a way of saying divide by zero, the result blows up to infinity, which is a pain for mathematicians. A simple illustration would be think of a simple function, something like

f(x) = x/(1 - x )

plot this and at x = 1 the result is undefined, it grows bigger and bigger as x -> 1, In special relativity such things occur because of the denominator sqrt(1 - (v/c)^2), When v -> c the denominator becomes zero, i.e. the result is undefined and the theory breaks down is all you can say at that point.

Often the math is far simpler to follow IMHO, rather than the written counterparts and the way in which some authors try to write ideas around such ideas. In Mathematics the definition is precise and to the point.

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If black holes were points of singularity then what do they mean "super massive black holes". A single point can only contain so much mass. Once this singularity has maxed out then an adjacent singularity becomes another black hole and the 2 black holes start orbiting each other really fast. At this point, the sucking in of more matter collides with the spinning black holes causing a massive ejection of energy called gamma ray blasts or something like that. I remember reading something about this in a book once.

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No - there is no limit to how massive a black hole can grow - only on the rate they can grow at. Supermassive black holes are millions of times heavier than the Sun, whereas stellar black holes are typically 5-30 times the mass.

Supermassive black holes have a larger event horizon, but they're still quite small - thats one reason we know they exist, there is something weighing a million suns in the middle of the galaxy occupying something less than the size of the solar system, and it's not visible... so the options are limited.

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...still these black holes still present an interesting problem. Consider the following experiment - if you throw a paperback copy of "Turn left at Orion" into a black hole then the information is "destroyed", a copy of the video "Leather Goddess of Hamburg" contains quite different information but chuck that in too and it ends up in the same state: see http://en.wikipedia.org/wiki/Black_hole_information_paradox . So, if the universe is a black hole it contains no useful information...

..only kidding!

P

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Hey!

..., but why do people think that black holes contain a singularity really?

// Andreas

Some people choose a description of blackholes that permit a singularity.

Some people choose a description of blackholes that don't permit a singularity.

According to Roger Penrose, "Nature abhors a naked singularity" ...

So pick whichever one you want and let whoever else pick the one they want, then don't argue.

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If black holes were points of singularity then what do they mean "super massive black holes". A single point can only contain so much mass.

Please bear in mind, the singularity and the event horizon are two different things. As more mass is added to a black hole, its event horizon increases in size due to the increased gravitational field.

As to whether there is a limit on how densely matter can be packed together, that's an open question.

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I used to have a copy of Adrian Berry's "Iron Sun - Crossing the Universe Through Black Holes". It was probably in the late 70's and I read it many times.

It was a good source of the scientific thinking of the day with a generous addition of speculation. Perhaps one of my favorite books. Sadly I gave my whole private library away to the public library about 10 years ago :( What was I thinking??

Anyway, From what I remember it would still be a good read today for those who want a non academic overview of black holes. I don't think Hawking Radiation had been invented/discovered at that time. Other than that the science hasn't moved on a great deal.

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No - there is no limit to how massive a black hole can grow - only on the rate they can grow at. Supermassive black holes are millions of times heavier than the Sun, whereas stellar black holes are typically 5-30 times the mass.

Supermassive black holes have a larger event horizon, but they're still quite small - thats one reason we know they exist, there is something weighing a million suns in the middle of the galaxy occupying something less than the size of the solar system, and it's not visible... so the options are limited.

If there is a limit to the rate of accretion (why?), then doesn't hawking radiation eventually balance out?.. maybe at 1000billion sol masses.. but could there be a limit, even if only theoretical?

Derek

Edited by rfdesigner
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It contains a singularity, because there is no known force to oppose gravity on the scale of these masses.

Below 1.5 solar masses (approx) the electron degeneracy pressure can resist gravity, making a stable system.

After that and below 3ish solar masses, the atoms themselves are crushed into neutrons, and that maintains a pressure outwards to counteract gravity (a neutron star). Past this point (with possible exception of quark stars), there is nothing left to resist the gravitational pressure, so it collapses in on itself to a singularity.

That said - no one really knows what goes on in a black hole, as no information can escape (probably!).

Anything with a radius/mass ratio < 2G/c2 will make a black hole. So to make one you either have to squash the radius of the object, or increase the mass (without changing the radius) - or both. For most black holes, it's the radius that decreases whilst the mass stays the same.

What if 'quark degeneracy pressure' created an object that resisted the force of gravity, but was still beneath the event horizon, and in supermassive black holes, maybe something that makes quarks has a degeneracy pressure, that can even resist the mass of billions of suns?

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What if 'quark degeneracy pressure' created an object that resisted the force of gravity, but was still beneath the event horizon, and in supermassive black holes, maybe something that makes quarks has a degeneracy pressure, that can even resist the mass of billions of suns?

There have been hypothesized some quark stars, a couple of candidates even proposed. However from what I understand the constraints are quite tight, leaving not a lot of room in the mass size between neutron stars and black holes for them to occupy, if indeed they are real. A good paper on them showing some of the detail is here

http://arxiv.org/abs/1210.1910

Back to Hawking radiation, the effects of this get less with bigger size - so from what I've read, Hawking radiation and the cosmic microwave radiation balance out at a black hole about the size of the moon. Such a black hole would lose about as much mass by Hawking radiation as it gains from absorbing photons from the CMB.

Below that size Hawking radiation gets more effective - which leads to the statement that if a black hole were created in the LHC, it would be so small it would evaporate almost instantaneously.

Meanwhile stellar mass black holes and above will continue to grow, some slowly, some more rapidly, but they'll grow until the universe runs out of energy, and then start to evaporate.

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What if 'quark degeneracy pressure' created an object that resisted the force of gravity, but was still beneath the event horizon, and in supermassive black holes, maybe something that makes quarks has a degeneracy pressure, that can even resist the mass of billions of suns?

An outside observer wouldn't be able to tell the difference. The internal structure of black holes remains entirely theoretical, hidden by the event horizon. As JulianO said early in the thread, no known force can resist gravity on this scale, including quark degeneracy pressure (if it exists). On the other hand, our understanding is incomplete. The string theory treatment of the problem yields a slightly different object called a fuzzball, which has no singularity. However, to an observer at a distance it would appear identical to a classical black hole - intriguingly, the maths works out to give the same radius for the event horizon.

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On June 26th, 9pm on BBC 2 there's a Horizon called "Swallowed by a black hole" which might be interesting.

Definitely interesting is that as a person falls into a black hole (feet first), the tidal forces which 'rip them apart' increase at such a rate so as to disallow the nerve impulses of pain from registering. The head-first swallowee will likely feel something.

I can't remember the precise details (size of BH, pain threshold, speed of pain etc) but this comes from J.A. Wheeler.

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Definitely interesting is that as a person falls into a black hole (feet first), the tidal forces which 'rip them apart' increase at such a rate so as to disallow the nerve impulses of pain from registering. The head-first swallowee will likely feel something.

So, when falling into a black hole, it's important to remember to brace your feet for impact?

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The tidal forces depend on the size of the black hole and are greater for small holes than big ones. Quote from Wikipedia:

The point at which tidal forces destroy an object or kill a person depends on the black hole's size. For a supermassive black hole, such as those found at a galaxy's center, this point lies within the event horizon, so an astronaut may cross the event horizon without noticing any squashing and pulling, although it remains only a matter of time, as once inside an event horizon, falling towards the center is inevitable. For small black holes whose Schwarzschild radius is much closer to the singularity, the tidal forces would kill even before the astronaut reaches the event horizon.[4][5] For example, for a black hole of 10 Sun masses[6] and the above-mentioned rope at 1000 km distance, the tensile force halfway along the rope is 325 N. It will break at a distance of 320 km, well outside the Schwarzschild radius of 30 km. For a black hole of 10,000 Sun masses it will break at a distance of 3200 km, well inside the Schwarzschild radius of 30,000 km.

http://en.wikipedia.org/wiki/Spaghettification

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