Black Hole and Quantum Tunnelling

[Sriman Dutta]

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.

[Daecon]

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

[geordief]

 

 

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, 2016 by geordief

[MigL]

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, 2016 by MigL

[Sriman Dutta]

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 ?

[geordief]

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, 2016 by geordief

[MigL]

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

[imatfaal]

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]

[MigL]

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, 2016 by MigL

[MigL]

And just to clarify, Imatfaal...

Mig is a shortening of my last name.

While L is my first initial.

Edited October 23, 2016 by MigL

[imatfaal]

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.