On the formation of black holes

Hello,

I’ve got a very unusual question.Today, it was stated to me by a friend that “if a coin is spun in absolute space without any exterior forces acting on it, its spin will accelerate to the speed of light and eventually form a black hole”.

Of course, to me that sounds preposterous. However, we are only 16 and his word is as good as mine. I don’t really see a connection between a coin spinning quickly and a massive dent in space-time.

Anyone?
Thanks

As a physicist who works in General Relativity, that sounds preposterous to me too. I’d be interested to know where he got it from. Also, what the heck is “absolute space”?

Uh, no, I don’t think so. Generally objects maintain their rotational inertia. So it would just keep spinning in the same direction at the same speed.

Of course, in the real world, it would run into electromagnetic radiation, which is a force of a kind; & be affected by any local gravitational effects, which are less a force than a…well, I don’t think we know really. But neither of those is likely to speed it up like that either. In fact gravity should slow it down one way or another: either by pulling it into another mass where it would come to rest, or, if the coin is in stable orbit, by tidal forces slowing it over eons.

I’m trying to think if EM radiation could increase rotational velocity somehow; but even if it could, I expect it wouldn’t ever push it to lightspeed (for esoteric physics reasons).

edited to add: This sounds like something your friend heard in a dream & thought sounded impressive.

I don’t know either. I asked him the same exact question.

I’d be curious to know where it’s gaining all that extra energy from. Sure you initially set the coin spinning with Energy = X but to speed it up to approach c E would wind up asymptotically approaching infinity.

There is a connection; the faster the coin spins, the greater the energy it has. The greater the energy it has, the more it will cause space-time curvature. But in practice this will be a tiny effect, and the coin would be ripped apart by centrifugal effects long before it could spin fast enough to form a black hole. Also, the coin would not spin faster without some external force acting on it.

But the spinning coin doesn’t gain energy by spinning faster, it gains energy by having more mass at the same speed.

No. Spinning faster => greater angular kinetic energy.

Does he agree that a faster spinning coin has more energy than a slower spinning one? If so, where is this energy coming from?

Conservation of momentum isn’t just a good idea; it’s the law!

Stranger

I don’t think so. “space-time curvature”, or what is commonly referred to as “gravity” is a function of mass. Not kinetic energy.

The curvature is caused by energy, not rest mass. More technically caused by the stress–energy tensor, whose components are energy and momentum densities and stress.

ETA: mass is of course, a large contributor of energy, since E=mc^2

A massive, rapidly spinning object will also distort the surrounding space, known as the Lense-Thirring precession , or colloquially as “frame-dragging”. This is an experimentally verified effect predicted by general relativity, but the effect should be immeasurable for such a low mass object regardless of the speed at which it rotates up to what is physically possible.

To comment on the o.p. “absolute space” is taken to mean a fixed background reference space against which all other motion and the action of physical mechanics is measured. Absolute space is an Aristotelian concept, and doesn’t even hold under Newtonian mechanics per Galilean invariance (that the laws of physics behave the same in all inertial reference frames; that is, frames that are not under external acceleration). General relativity extends this per Mach’s principle. It is widely accepted that there is no such thing in “absolute space”.

Stranger

Since no one mentioned it yet, I might as well give a McDonalds drive thru lesson in what a black hole is.

All objects with mass are attracted to each other with a force that is proportional to the square of the distances and the mass of the objects. IOW the larger and more dense the object, the harder it pulls on you.

This pull is actually a distortion of space time. Think of it like a bunch of different sized balls sitting on a mattress. The depression each ball causes is it’s gravitational effect.

Now as I said, gravity is a function of distance. Normally objects like the Earth are large enough relative to their mass that you hit the surface before you can get close enough to the gravitational center to feel any ill effects. However, if I were to compress the Earth to the size of your coin (don’t worry, I won’t), you would be able to get much closer to the gravitational center. So close in fact that once you get within a certain radius (called the “event horizon”) the pull of gravity is so strong it distorts space to the point you won’t be able to ever get back.

Think of it like the mattress model, but with one of the balls the size of a tennis ball but weighing several tons and punching a deep hole in (but not through) the mattress. It’s still there, but anything that rolls into that depression can never get out of the hole.
So if you kids still want to make a black hole, spinning a coin won’t work. You’ll need to compress an object about the size of a large mountain into a coin. Just check with your parents first.

Interesting.

Actually, if the OP and his friend make their OP coin, they can use this to produce a couple of gamma ray jets shooting out the poles.

In general realivity spacetime curvature is a function of the stress-energy tensor which most defintely does include terms ‘representing’ kinetic energy (infact it’s a bit more complicated than that, some of it’s components equal to the flux of total energy across surfaces in spacetime).

I don’t think it would be right to say that frame-dragging has been experimentally verified. .

As much as I like the general theory of relaivity I think sometimes the evidence in it’s favour is overplayed a little.

Again, as I tried to impart earlier: it’s not just rest-mass that determines space-time curvature. A spinning object will generate a greater gravitational field than a non-spinning object of the same rest-mass.

Just a hunch here: I suspect that where the OP says ‘absolute space’, he actually means ‘in a perfect vacuum, in perfect isolation from any external forces’.

(ETA: not that this makes a difference to the scenario)

Say what?

A derivation of the relativistic (frame-dragging) component of the anomalous precession of Mercury.

Gravity Probe A measures relativistic affect of altitude on the passage of time (measurement agreed with theory to 1:70*10[sup]6[/sup].

Gravity Probe B measures frame-dragging effect to within 15% of theory
STEP program to measure equivalence between inertial and “gravitational” (coupled response) mass

Frame-dragging is a very subtle effect compared to other effects, but measurements have established that it occurs independent of any other explanation to a degree that it is uniformly accepted among the physics community. The collective effects of general relativity have been verified to a precession that is exceeded in the natural sciences only by the measurement of the Lamb shift and the anomalous electron magnetic dipole moment in comparison to predictions by quantum electrodynamics. It is one of the most thoroughly verified theories in physics and anything that would possibly challenge it would have to look very much like general relativity in its effects and interactions.

Stranger