Hi everyone,

It might be very impractical but still I want to ask it.

When a ray of light enters a perfect hypothetical reflecting box through a small hole ( that doesn't diffract it), the ray gets trapped if that hole is closed soon. However due to the very strange phenomenon of quantum tunnelling the light ray may come out ( i.e. tunnel out) if we are to leave the box undisturbed for infinite period of time. So the inference is that a light ray cannot be trapped within a closed box for infinite period of time.

Now let's take the case to a black hole.

A ray of light approaches the event horizon of a supermassive black hole. It enters into it and gets trapped within a very weird space-time curvature inside the black hole. So will this ray of light escape out of the event horizon by quantum tunnelling?

Thanks in advance for your thoughts.

The Wikipedia article on Hawking radiation mentions something similar involving quantum tunnelling.

 

 

The Wikipedia article on Hawking radiation mentions something similar involving quantum tunnelling.

Yes I saw that too.

 

It seems that Quantum tunneling is one way of modeling Hawking Radiation which has been predicted (but not confirmed,so far as I know)

 

 

 

"In another model, the process is a quantum tunnelling effect, whereby particle–antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon."

 

https://en.wikipedia.org/wiki/Hawking_radiation

 

I cannot see in the article above that photons escape . It seems to mention particle-antiparticle pairs.

Edited October 22, 20169 yr by geordief

This mechanism would be applicable for massless particles, i.e. EM radiation. But Hawking radiation can also consist ( to a small degree ) of massive particles.

For massive pairs of virtual particles, the problem essentially reduces to an infinitely deep square well potential, for which ( as Swansont pointed out in another thread ) there are no tunneling solutions.

( This is because it would require infinite energy for massive particles to achieve escape velocity )

 

That is why I sometimes hesitate to use the tunneling model for Hawking radiation

Edited October 22, 20169 yr by MigL

So quantum tunnelling is one of the ways of putting erect the hypothetical concept of Hawking radiation.

But what actually happens inside a black hole, since not all the mass and energy trapped within gets radiated out ?

So quantum tunnelling is one of the ways of putting erect the hypothetical concept of Hawking radiation.

But what actually happens inside a black hole, since not all the mass and energy trapped within gets radiated out ?

 

 

I thought it did...............................eventually. Are you sure it doesn't?

Edited October 22, 20169 yr by geordief

Hawking radiation is proportional to the BH's temperature and inversely proportional to its size.

Hawking radiation is proportional to the BH's temperature and inversely proportional to its size.

 

Not sure what you are getting at there Miguel. What feature of the radiation?

 

A black holes temperature is the temperature of the black body which would emit Hawking radiation of that spectrum

 

[latex]T = \frac{1}{M} \cdot \frac{\hbar c^3}{8G \pi k}[/latex]

 

The temperature of the black body / black hole is inversely proportional to the Mass.

 

The size (radius) of the black hole is obvious linearly proportional to the mass

 

[latex]r=M \cdot \frac{2G}{c^2}[/latex]

I.E. a smaller BH is 'hotter' and will radiate more mass/energy, while a large one is 'cool' and will radiate very little mass/energy.

 

So a large BH will persist for immeasurably long times, while a small one will radiate away in relatively few ( still billions ) of years.

 

Or as a BH gets smaller its energy output increases and it evaporates faster and faster.

Edited October 22, 20169 yr by MigL

And just to clarify, Imatfaal...

Mig is a shortening of my last name.

While L is my first initial.

Edited October 23, 20169 yr by MigL

And just to clarify, Imatfaal...

Mig is a shortening of my last name.

While L is my first initial.

 

I am so disappointed - I said your user name once in my head and had a lightbulb moment; now I find out that I have deluded myself for years.