[K.I.L.E.R]

According to General Relativity (the theory that predicts, and explains most of the features of black holes), there is no lower limit to the size of a black hole. But, a full theory of how gravity works must also include quantum mechanics, and such a theory has yet to be constructed. Some hints from recent work on this theory suggest that a black hole can be no smaller than about "10-to-the-(-33)" cm in radius --- 0.000000000000000000000000000000001 cm. On that small a size scale, even the apparently smooth nature of space will break down into a "rat-trap" of tunnels, loops, and other interwoven structures! At least, that's what current work suggests.

So what can a blackhole that size do?
If I step on it will it destroy me?

Actually, I heard 1 theory that the smaller the blackhole, the more powerfull it's tidal forces are. Does this stand true today?

[DemoCoder]

The smaller the blackhole, the faster it will evaporate. A super small blackhole won't last vast long.

[Crusher]

If I step on it will it destroy me?

Yes

Anything that has a mass great enough to create an event horizon has enough gravitational force to pull you into it. Size doesn't matter in gravity, only mass and distance.

Originally Posted by DemoCoder

The smaller the blackhole, the faster it will evaporate. A super small blackhole won't last vast long.

Unless there are people stepping on it all the time, adding to it's mass and allowing it to grow

[pcchen]

A black hole that small will be less than 10 microgram, and because it's so small it is quite hard to hit one even for an atom. So I think it wouldn't be very dangerous. However, such a small black hole is likely to explode in very short time, and the energy would be quite large so it's still very dangerous.

[Vince]

Originally Posted by Crusher

Yes, Anything that has a mass great enough to create an event horizon has enough gravitational force to pull you into it. Size doesn't matter in gravity, only mass and distance.

It was my understanding that according to Roy Kerr's solution, a rotating 'Black Hole' (eg. that unlike Schwarzshild's which were static and not representative of those in nature) doesn't collapse to a point, but rather a ring, with it's own set of unique properties. For example, due to the curvature of space-time, any matter approaching the ring from it's spatial side will hit the ring and be destroyed as the gravitational 'force' applied would be infinate. Where as if you'd enter perpendicular and 'threw' the ring's axis of rotation, the effects duie to the curvature of space-times topography would be massive, but finite.

So, in a physical sence you'd be toaat - but in a theoretical sence there is no infinate value preventing travel talong the axis of rotation in a Kerr Blackhole.

Originally Posted by K.I.L.E.R

Some hints from recent work on this theory suggest that a black hole can be no smaller than about "10-to-the-(-33)" cm in radius

Better known as Planck's Length... good thing to memorize and impress your friends 1.6*10^-35 m.

Also, I allways assumed that QTheory alone wouldn't be powerfull enough to solve the Quantum effects (Quantum Corrections, et al) happening and we'd need 10d String Theory+ to solve it. But, I'm probobly hopelessly out of date

[Bogotron]

Vince

For example, due to the curvature of space-time, any matter approaching the ring from it's spatial side will hit the ring and be destroyed as the gravitational 'force' applied would be infinate.

Rule of thumb: If you get something infinite out of a physics equation, you're doing something wrong.

Getting infinites out of physics equations/theories is more a sign of the system being fed invalid parameters or that the system can't describe the phenomenon in question.

[nutball]

Originally Posted by Crusher

Anything that has a mass great enough to create an event horizon has enough gravitational force to pull you into it. Size doesn't matter in gravity, only mass and distance.

That's a common misconception about black holes. Not helped by the way they are reported in the media, or dealt with in science fiction.

A black hole with the mass of a tennis ball has the same gravitational field as a tennis ball the size of a tennis ball (to first order). When was the last time you were sucked into a tennis ball? The fact that it's a black hole does not make it the super-mega-death killer that the screaming media would like to have you think.

There are two "magic" things about black holes: firstly density (which is what makes them black holes), and secondly the BHs we can detected (directly or indirectly) tend be exceeedingly massive (from a Solar mass to 100s of millions of Solar masses). A 10^8 Solar mass black hole exterts a very powerful gravitational influence on its surroundings, but then so would anything with a mass of 10^8 Solar masses. What makes a black hole different is that you can pack that mass into a very small volume. The fact that it's a black hole doesn't make it more dangerous per se, you need to take into account the mass too.

[K.I.L.E.R]

nutball, so I can step on a black hole the size of a tennis ball without it killing me?

[epicstruggle]

why is everyone stepping on black holes (regardless of size), are we so bored with life that we need a challenge.

later,

[pcchen]

Originally Posted by K.I.L.E.R

nutball, so I can step on a black hole the size of a tennis ball without it killing me?

No, a black hole of the size of a tennis ball should be very heavy (likely heavier than the earth). That will definitely kill anything in proximity.

However, a black hole of the mass of a tennis ball should be very small (perhaps smaller than an electron). It would be very hard to step on one.


I don't know why would one want to step on a black hole, though. However, it would be interesting to see what happens when one get into a very huge black hole (radius of several thousand light years).

[nutball]

Originally Posted by K.I.L.E.R

nutball, so I can step on a black hole the size of a tennis ball without it killing me?

Yes, in fact you could quite safely play tennis with it. Might be a bit frustrating though.

Edit: assuming you mean mass of a tennis ball.

[Crusher]

Right, except that in order for it to be considered a black hole, it needs to have a high enough mass to invoke a gravitational field that is so powerful that light cannot escape it, which to me implies a mass significantly greater than a tennis ball, as I don't think the mass of a tennis ball can be made dense enough to do that. But if it could, I don't think you could play tennis with it. I think instead, it would enter a chain reaction where it absorbed all the atoms from the atmosphere, you (when you step on it), and eventually the entire mass of the earth (it would probably stop there... might get the moon too).

If it's strong enough to capture light, it's strong enough to keep pulling atoms from everything it comes in contact with, and I don't think it would 'evaporate' unless it started in the middle of nothing to begin with, and had no matter nearby to absorb, in which case you wouldn't have to worry about stepping on it. But we'll ignore that situation, just as we're ignoring the fact that we don't posses the incredible ammount of energy required to compress the mass of a tennis ball into an imperceptibly small, incredibly dense object that light cannot escape from.

[nutball]

Originally Posted by Crusher

Right, except that in order for it to be considered a black hole, it needs to have a high enough mass to invoke a gravitational field that is so powerful that light cannot escape it, which to me implies a mass significantly greater than a tennis ball, as I don't think the mass of a tennis ball can be made dense enough to do that.

Escape velocity is given by the equation v = sqrt(2 * G * M / r), where G is the gravitational constant, M is the mass of the body in question, and r is its radius. For any non-zero M there is a radius r for which v > c (c = speed of light). Ergo in principle any mass M can have an event horizon.

The key to creating your black hole is squashing the matter down to a small enough r. Black holes form in nature because you run out of forces to support them against their own weight. White dwarf stars are supported against their own weight by electron degeneracy pressure. At a given mass (the Chandrasekar limit) this gives way and the star collapses to form a neutron star, which is supported by neutron degeneracy pressure. Increasing the mass still further you run out of forces, and the star collapses to form a black hole.

Clearly a tennis ball can't collapse under its own weight naturally, so such things are unlikely to form naturally. However this doesn't mean that a black hole with the mass of a tennis ball isn't theoretically possible.

I think instead, it would enter a chain reaction where it absorbed all the atoms from the atmosphere, you (when you step on it), and eventually the entire mass of the earth (it would probably stop there... might get the moon too).

There you go with your science fiction again! A black hole the mass of a tennis ball would orbit the Earth like a tennis ball with the mass of a tennis ball. The Earth and the atmosphere would probably notice a tennis ball mass black hole less than it would a tennis ball mass tennis ball.

If it's strong enough to capture light, it's strong enough to keep pulling atoms from everything it comes in contact with, and I don't think it would 'evaporate' unless it started in the middle of nothing to begin with, and had no matter nearby to absorb, in which case you wouldn't have to worry about stepping on it. But we'll ignore that situation, just as we're ignoring the fact that we don't posses the incredible ammount of energy required to compress the mass of a tennis ball into an imperceptibly small, incredibly dense object that light cannot escape from.

A tennis ball mass black hole would be incredibly small, and it's cross-section of interaction would be similarly tiny. It would be more likely to pass completely unnoticed between the atoms which constitute the Earth and its atmosphere.

[Crusher]

Originally Posted by nutball

Escape velocity is given by the equation v = sqrt(2 * G * M / r), where G is the gravitational constant, M is the mass of the body in question, and r is its radius. For any non-zero M there is a radius r for which v > c (c = speed of light). Ergo in principle any mass M can have an event horizon.

Could be wrong, but I'm pretty sure that's not true, since for most objects the value of r would be less than the diameter of the object, and I don't think that equation holds true inside the boundry of the massive object.

Originally Posted by nutball

A tennis ball mass black hole would be incredibly small, and it's cross-section of interaction would be similarly tiny. It would be more likely to pass completely unnoticed between the atoms which constitute the Earth and its atmosphere.

I still think that would only be the case if it weren't a "true" black hole... that is, if the value of r from the equation above is noticably larger than the radius of the object itself, I think it would pull atoms out of the atmosphere, soil, human body, etc. If light particles can't escape it, surely a neighboring atom must be susceptible to its pull as well. If it can't even do that much, then I don't see how it could possibly remain in a state at which it could be considered a black hole for any measurable ammount of time.

[K.I.L.E.R]

I would give anything to step on a blackhole. Especially one with the mass of a tennisball.

[nutball]

Originally Posted by Crusher

Could be wrong, but I'm pretty sure that's not true, since for most objects the value of r would be less than the diameter of the object, and I don't think that equation holds true inside the boundry of the massive object.

The distinction you draw is pretty much the distinction between something which is a black hole and something which isn't!

The expression is correct, though you have to understand that the M is the enclosed mass, ie. the mass enclosed within radius r.

For most everyday objects what you say is true, they are larger than r. If they were smaller than r they'd be a black hole. By definition.

[K.I.L.E.R]

How do you guys know so much?
I assume you are all older than I am (I'm 18) and have degrees or such? Or are as bored as I am?

[arjan de lumens]

A combination of education, natural curiosity, I suppose, and possibly boredom as well, as you mention. For black holes specifically, you could look here for a somewhat informal introduction to the subject.

[nutball]

Originally Posted by K.I.L.E.R

How do you guys know so much?
I assume you are all older than I am (I'm 18) and have degrees or such? Or are as bored as I am?

A PhD in astrophysics helps

[Crusher]

Stay in school! heh

I only had 2 semesters of physics, and I don't even remember if we studied black holes specifically, but you still learn a lot of basic principles that help you understand more complex situations. I'm sure nutball has a better knowledge of them than I do, I was just trying to apply common sense and reason my way through justifying my previous claim. About the only thing I have left that would help my case would be to find the average mass of a tennis ball, determine what radius such a mass needs to be compressed to in order to create an event horizon, and then compare that size to the distance between atoms in the atmosphere to see how likely it would be to start pulling the earth into it. I don't really care about the argument enough to go that far, though.

[DemoCoder]

Blackholes show that an object's "size" is pretty much an illusion. Matter can be compressed much smaller than its "natural" size, just look at the compression ratio between a neutron star and its uncompressed state.

At some point, the gravitational force becomes so large that not even the degeneracy pressure between electrons or between neutrons, et al, can resist, and eventually there is nothing to stop the collapse.

In highly compressed states, matter behaves more like waves, and the idea that matter acts like little marble spheres you learned in high school chemistry or physics, where they have a defined volume/radius, and cannot occupy the same place at the same time, goes out the window.

Bose-Einstein condensate also shows how you can coax atoms to lose their identity and huddle closer together.

By definition, any object whose radius is smaller than its Schwartzchild radius is a blackhole.

[BlackAngus]

Hey all!
Ive read b3d fourms for quite a while now , and usually have nothing to say. (still dont really). But I have to say you are all FREAKS!!!!!!!
With that said this thread made me join up.
I just wanted to say some of you guys are brains, and thanks for some of the links here to good articles and lectures.
Hopefully Ill have something more constructive to add in the future. =)

BA

[Fred]

Semi classically, you can have Microscopic black holes. In fact the Large Hadron Collider in Cern (due in 2006) that accelerates particles to the TeV scale might indeed form tiny black holes. If you pack enough energy in a small enough space (past the schwarschild radius) you'll get a black hole.

These will evaporate and leave a spectrum that should in principle be detectable.

The thing is, its a little bit hazy in the case of a microscopic bh because quantum field theory is not really sufficiently advanced to fully understand the properties.

String theory is an attempt at Quantum gravity, but it still has a ways to go. There are other alternatives, like loop quantum gravity, Non commutative geometries, etc etc

Personally I don't like String theory, it irratates me at this stage frankly, its still extremely raw. Ill give a link to a summary of that in a few

As for singularities in general relativity and black holes. One has to understand that its a little bit complicated. One can in general, rewrite the metric so that certain traits of the singularity are removed. In the case of a schwarschild bh, these are called UV coordinates or Kruscal Schecheres coordinates

[Bigus Dickus]

Out of curiosity, does someone know the equation describing how Hawking radiation relates to the mass of a black hole? All this talk about a tennis ball mass black hole has me wondering how long such a microscopic black hole could survive before vaporizing itself. I'm guessing a very, very short time.

As interesting as miniature black holes are, I find the concept of extremely large and relatively low density black holes to be equally fascinating. It is possible for a black hole to be "black" without the gravity inside causing matter to collapse to a point (or whatever the "correct" theory of quantum gravity will ultimately reveal that it collapses to)... at least not for a relatively long time. If our universe is closed (which, at the moment, it doesn't appear to be), then it could be considered a black hole, and would appear as such to an outside observer (or so I'm thinking... I could be missing a crucial distinction there).

[arjan de lumens]

Using a few formulas I found here and here the amount of Hawking radiation and the lifetime of a black hole can be computed rather straightforwardly. For a black hole with the mass of a tennis ball, I get a lifetime of about 10^-19 seconds, give or take an order of magnitude or so. Which indicates that even if you managed to create such a beast, it would immediately explode with the power of a medium-size nuclear weapon.