## Making a Black Hole with Light

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lgw
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### Making a Black Hole with Light

What if you could focus all the light from the Sun, or from some number of stars, sharply enough to create a black hole at the focus. This would be a fun addition to discussions about radiative thermal equilibrium ("technically, if you focus the light sharply enough, it's actually much cooler, so you don't always get thermal equilibrium").

To do so would just require enough energy density - enough mass-equivalence in the light to be its own Schwarzschild radius. I started with the idea of an Earth-mass black hole: that would require about 5.4 * 1041 J of light energy inside a radius of about 8.8 * 10-3 m. If we imagine a 1 W light source shining in a focused beam, that's 1 J smeared out across 3 * 1010 cm, so a 3 * 1010 W light source focused on our target point should give us about 1 J of energy inside the critical radius.

So, it's just a matter of getting about 1.6 * 1052 W of light, arranged as a sphere shining inwards, and we'll have our black hole. Sadly, that's about 4.2 * 1025 times the Solar luminosity, so even before redshift there's not enough visible light in the universe. (Anyone know the total energy of the CMBR in the visible universe?) So we'd need to optimize a bit - perhaps we can just trigger 1016 Supernovae simultaneously inside a mirror box? What if we tried for a different mass of black hole?

That's where I discovered something fun: the "1.6 * 1052 W of light" number works for any size black hole. Schwarzschild radius scales linearly with mass, and the amount of focused light energy currently transitioning a sphere around the focus also scales linearly with radius. So, if you have a shell of light sources all focused at the center, then the needed luminosity is the same regardless of the radius of the black hole. When you turned the experiment on, you'd get a black hole as the light reached the center, which would grow at the speed of light (feeding on the incoming energy) until it consumed the apparatus. Proving me wrong after all: you would get thermal equilibrium between the light sources and the focus.
"In no set of physics laws do you get two cats." - doogly

FancyHat
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### Re: Making a Black Hole with Light

You'd like to make a kugelblitz?
I am male, I am 'him'.

quantropy
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### Re: Making a Black Hole with Light

Suppose that you had so many stars that in whatever direction you looked you saw the surface of a star at a temperature of 5,778 K. Then you would soon warm up to 5,778 K. The thing is though that the second law of thermodynamics says that focusing isn't going to get you a higher temperature, so presumably that limits the possibility of focusing a large amount of energy.

In the more reasonable situation where there are gaps, you could set up a heat engine to use the difference in temperature between the 5,778 K surfaces and the dark sky, and so create concentrated energy that way. That doesn't count as focusing though. In fact we could do something along these lines at present. The power from a large array of solar panels fed into a collection of lasers might be able to create a black hole if the lasers are powerful enough.

lgw
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### Re: Making a Black Hole with Light

quantropy wrote:Suppose that you had so many stars that in whatever direction you looked you saw the surface of a star at a temperature of 5,778 K. Then you would soon warm up to 5,778 K. The thing is though that the second law of thermodynamics says that focusing isn't going to get you a higher temperature, so presumably that limits the possibility of focusing a large amount of energy.

None of that seems right.
• The Stefan–Boltzmann law tells us that the power emitted by blackbody radiation per surface area is a function only of temperature (the fourth power of temperature times the Stefan–Boltzmann constant).
• The second law of thermodynamics tells us only that the system will be in thermal equilibrium, not what its temperature will be (otherwise, if temperature were capped, you couldn't make a solar-powered electric heater above 6000K).
Consider a uniform shell of N Sun-like stars - once it reached thermal equilibrium: the temperature would be such that N * 3.8 * 1026 W was emitted from the given surface area. Contrast a uniform ball of N2 Sun-like stars of the same radius: the temperature would be such that N2 * 3.8 * 1026 W was emitted from the same surface area. If we increase the total energy by 104, the temperature has to be 10 times as high at thermal equilibrium.

In the same way, focusing light onto a small target must raise it's temperature. If you focus all the energy of the Sun on a target with 10-4 the surface rea, the target must be 10 times as hot as the surface of the Sun to reach thermal equilibrium through blackbody radiation.

All that aside, we know that if you try to force too much light energy into a given volume it won't happen, but the way it won't happen is a black hole (and doing that math for a single photon gives us the Planck units, of course).
"In no set of physics laws do you get two cats." - doogly

quantropy
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### Re: Making a Black Hole with Light

lgw wrote: If you focus all the energy of the Sun on a target with 10-4 the surface rea, the target must be 10 times as hot as the surface of the Sun to reach thermal equilibrium through blackbody radiation.

But if you've got a system which will focus radiation in that way, then presumably I can use it to focus the radiation from a room temperature object on to another object to make it hotter than the original object. Then I just connect a heat engine between them and get a continuous output of useful energy.

stianhat
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### Re: Making a Black Hole with Light

Also, since this means absorption + emission + reflection is no longer = 1, I will put a highly absorbant material next to a highly emittant material, contain them inside a highly reflective material, connect the first two materials to a heat engine and forever reap the benefits. And also, while doing it, I will also create negative kelvin temperatures. No need for two nobel's prizes, I will make do with just one, thank you very much.

/sarcasm off, friendly mode ON

Igw, you cannot focus light to create higher temperatures than the original. If you focus light from A onto B, and B is hotter than A, the sum of energy will flow in the *reverse direction* through the same lens (from B towards A). The Constitution of the Universe (Laws of Thermodynamics) stipulate that (a system of) two bodies are at equilibrium when at the same temperature. When not in equilibrium, all spontaneous processes will go towards aforementioned equilibrium.

It may be slightly more complicated , considering collimation and such but tbh, that is the easiest/simplest explanation that i can conjure without feeling like i am walking on a thin patch of ice.

Xenomortis
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### Re: Making a Black Hole with Light

lgw wrote:The second law of thermodynamics tells us only that the system will be in thermal equilibrium, not what its temperature will be (otherwise, if temperature were capped, you couldn't make a solar-powered electric heater above 6000K).

Being in thermal equilibrium means being at the same temperature.
Note that a solar furnace does indeed have an upper limit on the temperature of its target - the surface temperature of the Sun (treating it as a black-body, which isn't quite accurate).
A solar powered heater is not under such a restriction; a heater powered by photovoltatic cells could indeed reach temperatures exceeding the Sun's surface temperature, but the energy out will be less than the energy in.

Edit:
This feels strangely familiar.

Xanthir
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### Re: Making a Black Hole with Light

Xenomortis wrote:Edit:
This feels strangely familiar.

Yup. And to save people some reading, the intuitively-convincing takeaway is that lenses are bi-directional. Whenever you focus energy from object A to object B, you're *also* focusing energy from B back to A. Once B reaches the same temperature as A, both objects are feeding the same amount of energy to each other, and you don't gain any more temperature.
(defun fibs (n &optional (a 1) (b 1)) (take n (unfold '+ a b)))

HungryHobo
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### Re: Making a Black Hole with Light

There's an arxiv paper on this

http://arxiv.org/pdf/0908.1803.pdf
In a previous paper by the first author [9], it was proposed that a SBH could
be artificially created by firing a huge number of gamma rays from a spherically
converging laser. The idea is to pack so much energy into such a small space
that a BH will form. An advantage of using photons is that, since they are
bosons, there is no Pauli exclusion principle to worry about. Although a laser-
powered black hole generator presents huge engineering challenges, the concept
appears to be physically sound according to classical general relativity. The
Vaidya-Papapetrou metric shows that an imploding spherically symmetric shell
of “null dust” can form a black hole (see, e.g., [3], p. 187, or Joshi [10] for
further details).

Since photons have null stress energy just like null dust, a black hole should
form if a large aggregate of photons interacts classically with the gravitational
field. As long as we are discussing regions of spacetime that are many orders
of magnitude larger than the Planck length, we should be outside of the regime
of quantum gravity and classical theory should be appropriate. However, the
assumption of spherical symmetry is rather special, and an investigation into
the sensitivity of the process to imperfections in symmetry is an interesting
problem for classical general relativity. If a high degree of spherical symmetry
is required, then this could pose serious engineering challenges.
Since a nuclear laser can convert on the order of 10^−3 of its rest mass to
radiation, we would need a lasing mass of order 10^9 tonnes to produce the
pulse. This should correspond to a mass of order 10^10 tonnes for the whole
structure (the size of a small asteroid). Such a structure would be assembled in
space near the sun by an army of robots and built out of space-based materials.
It is not larger than some structures human beings have already built. The
precision required to focus the collapsing electromagnetic wave would be of an
order already possible using interferometric methods, buton a truly massive
scale.

This is clearly extremely ambitious, but we do not see it as impossible.

Give a man a fish, he owes you one fish. Teach a man to fish, you give up your monopoly on fisheries.