Can a black hole form using only photons - in theory?

[cybernomad]

(Still a newbie here so pardon my naivety.)

Now if possible, this question asks what’s the minimum mass-energy required and if you like, for a black-hole that exists at least 1 second.

If not possible why?

Also a side question. Can 2 or more photons occupy the same space?

 

[pervect]

You can form a black hole using only radiation (photons) if you have a sufficient amount of energy in the center-of-momentum frame.

A beam of radiation propagating in a single direction (or a single photon, no matter how high its energy) will not form a black hole.

However, a collection of radiation from all directions, focused onto a spot in space, could theoretically form a black hole.

If you are using visible light, the smallest black hole you could make would have a Schwarzschild radius of something near the wavelength of the light used to form it. (This is just a rough approximation). Since R= 2M (in geometric units), the mass would be R/2 * (c^2/G) in standard units.

Taking R to be .5 micron, we get 3*10^20 kg, multiplying by C^2 this is 3*10^37 joules.

This is an enormous amount of energy - for reference, the mass of the Earth is about 6*10^24 kg.

I'd have to look up the evaporation formulas to figure out the lifetime.

 

[Wizardsblade]

Could you theoreticaly use lasers to creat a standing waves capable of creating many consecutive balck holes?

 

[cybernomad]

A beam of radiation propagating in a single direction (or a single photon, no matter how high its energy) will not form a black hole.

why s that?

If you are using visible light, the smallest black hole you could make would have a Schwarzschild radius of something near the wavelength of the light used to form it. (This is just a rough approximation). Since R= 2M (in geometric units), the mass would be R/2 * (c^2/G) in standard units.

Taking R to be .5 micron, we get 3*10^20 kg, multiplying by C^2 this is 3*10^37 joules.

What if the photons were high energy gamma rays, would it shrink the Schwarzschild radius? Would it require less mass-energy?

 

[Physics Monkey]

cybernomad, if you have a beam of light (or a single photon) propagating in the +z direction, then in a coordinate system moving in the +z direction at high speed, the energy (and momentum) of the beam tend to zero. You can check this for yourself by simply Lorentz transforming the photon's four momentum to the moving frame. Since in this frame of reference the beam has no energy, the beam of light can't produce a gravitational field. On the other hand, two counter propagating beams would produce a gravitational effect. Can you explain why the argument I gave above is no longer valid?

Of course, a universe with just an infinite beam of light in it isn't very physical, so these kinds of considerations are somewhat artificial.

Edit: clarified a few things.

 

[cybernomad]

Can you explain why the argument I gave above is no longer valid?

no, I'm just curious but thanks for your reply.

Of course, a universe with just an infinite beam of light in it isn't very physical, so these kinds of considerations are somewhat artificial.
Edit: clarified a few things.

yes, it's just mainly a theoretical musing.

 

[NateTG]

Could you theoreticaly use lasers to creat a standing waves capable of creating many consecutive balck holes?

Theoretically, it could be done with light bulbs.

 

[pervect]

why s that?
What if the photons were high energy gamma rays, would it shrink the Schwarzschild radius? Would it require less mass-energy?

Take a look at, for instance, the FAQ http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html" (This is about what happens with high speed particles, but you can think of light as the limiting case of a particle with less and less rest mass going faster and faster).

With high energy gamma rays, you could use less mass (lower energy). The Schwarzschild radius scales linearly with mass, so if you halve the radius, you halve the reqiured mass.

 

[pervect]

Could you theoreticaly use lasers to creat a standing waves capable of creating many consecutive balck holes?

I very much doubt it. For one thing, there is a critical field intensity at which your laser beams would start to create particles, the Schwinger critical field. So if you try to do the job with one laser, it would have to be very large physically to keep the beam intensity below this limit.

In addition, I strongly suspect that the resulting system would be unstable in the sense that as soon as one black hole started to form, it would absorb all the energy.

Of course this is rather speculative, I haven't worked out any of the details (but the whole scenario is pretty unlikely).

I think you'd have much better luck with about 10^31 or so megajoule lasers (if they were designed to produce very short, femtosecond pulses, otherwise you'll need more lasers) all aimed at the same spot within a half-micron precision :-).

[add]
Even with this approach (a Very large number of focused pulsed lasers) you still might have problems with the Schwinger critical field being exceeded and the resulting particle creation "bleeding" too much energy away from the beam before the black hole density at the center could be reached. I have no clue how to go about calculating this effect, unfortunately.

I don't seem to have any good references for the Schwinger field, which is of course a quantum phenomenon rather than a GR phenomenon. The abstract below at least talks about proposals to exceed it.

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000091000008085001000001&idtype=cvips&gifs=yes

 

[pervect]

A more reliable way to form a black hole out of light might be this, on second thought:

Convert about 300,000 solar masses to radiation, and concentrate the resulting radiation within a radius of about 880,000 kilometers. Unless I've missed a decimal point somewhere (quite likely!) this will keep the electric field intensity below the Schwinger limit. This is of course a much larger black hole than the first one which assumed we could concentrate radiation more densely without any problems.

The formula I pasted into google calculator to get this was

1/sqrt(64*(permittivity of free space) *
(10^18 volts/meter)^2/c^2*(G/c^2)^3)=

The factor of 64 came from taking (rho+3P) * 4/3 pi (2M)^3 = M and solving for M, noting that pi was roughly 3.

The pressure P of the EM field is .5 (permitivity of free space) * E^2 where E is in volts per meter, and rho = P/c^2