Thread: Shrinkage of black holes.

I'm trying to remember what the official theory was on this. I'm curious why it's a surprise for black holes to emit radiation of some kind?

I would think that higher wavelenth light would have higher kinetic energy, despite not having a higher velocity, and since gravity is defined by force (not just acceleration), it would seem like some very high wavelenths of light would be able to escape.

It all comes down to my misunderstanding light, though, I guess. Does the fact higher wavelenths of light have more (relativistic) mass work against this?

Hi kojax,
The shorter the wavelength the higher the energy. The equation is E=hc/lambda where h=Planck's constant, c=speed of light, & lambda=wavelength.

Whether something escapes from a gravitational field, as far as I know, only depends on its velocity. To see this, set the kinetic energy equal to the potential and solve for velocity. You should see that the mass of the escaping object is irrelevant and that this escape velocity only depends on the mass of the object creating the gravitational well (e.g., the black hole) and the distance from this object.

Notice that (once you have solved this) on one side of the equation we have something that is a property of only the escaping object (velocity). And on the other side we have some stuff that are properties of only the object that we are escaping from (M). (...and of course the separation is a mutual sort of thing.)

In simpler terms, the only variable that we have control over (if we are the escaping object that is) is velocity. And guess what... we can't go faster than c.

So it is not necessarily the energy we possess, but our velocity that determines if we escape (albeit usually they go hand in hand...).


By the way... I think you were thinking about Hawking radiation. This has to do with quantum mechanics and magical shit.

And as to your original question "why is it a surprise...", before Hawking mucked everything up with QM it was thought that nothing could escape because in order to, it'd have to go faster than c.

That's my take anyway....

Cheers,
william

Alright, but here's what throws me: Gravity is a force, not a constant of acceleration.

An object traveling with a short wavelength has a higher kinetic energy than what it's linear velocity would normally indicate.

In other words, it takes more force to slow it down than it would to slow an object traveling at the same speed, but with a longer wavelength.

So, having a longer or shorter wavelength should alter a photon's ability to escape gravity wells.

Just to clarify, nothing can escape the gravitational pull of a black hole and that is why hawking radiation is surprising. However, hawking radiation is not actually radiation that is emitted by the black hole, but radiation that is created around the event horizon of a black hole due to quantum ground state fluctuations. So to an observer it would seem as though the black hole was radiating energy even though strictly speaking it wasn't.

I hope that makes sense!

It does, but I'm still lost on how it can prevent extremely short wavelenths of light from escaping. (Perhaps at a very slow rate?)

The shorter the wavelenth, the more gravity it would take to prevent it from escaping. (A longer amount of exposure to a given force is needed to cause the same decelleration)

Wouldn't it be possible, if a beam of light (or single photon of light) inside the event horizon were to gain enough kinetic energy, for it to escape?

The concept of a black hole is that nothing can escape from inside the event horizon!

As william says, wether an object avoids being captured by the gravitational pull of the black hole (or any thing for that matter) is dependent on its velocity (since kinetic energy is proportional to speed). Since all photons travel at the same speed, the wavelength of the light is irrelevant.

The key is to remember that all photons have the same kinetic energy. Although different wavelengths of light have different energies, the difference in energy is not kinetic - it's a form of potential energy (I think). So the effect of a gravitational field is the same on all photons.

I have written this in somewhat of hurry, so if I have misunderstood your query, I apologise. Also, If I have written anything erroneous I hope someone will correct me.

Thanks

Oh. I see. That's what had been throwing me. Higher energy light doesn't have a higher kinetic energy, just plain a higher energy in general (or by some kind of energy estimation)?

What would really resolve the question as far as whether gravity affects different wavelenths differently would be to know if the light bent by distant gravity lenses, or in the solar eclipse experament had been separated into separate bands like when it passes through a prism.

I can't seem to find anything that comments on this, so I'll have to assume it doesn't happen.

Another interesting question would be whether light moving directly away from a massive body (other than a black hole) is slowed by its gravity, or merely increases in wavelength, but continues moving at the same speed.