# Can light be somehow confined to create a kugelblitz?

Imagine we want to create a kugelblitz (a black hole generated by light) by focusing multiple laser beams to the same point in outer space. If I'm not wrong, the beams would simply cross each other at the focus point. Does it mean that, in order to create e.g. a kugelblitz with a 0.1 light-second (30,000 km) Schwarzschild radius, our only option is to synchronize the lasers so that all the necessary energy reaches the focus within 1/10th of a second? Or could light somehow (through interaction between the beams?) get confined in a region of space, so that we could use longer pulses to more slowly build up the needed energy?

• Commented Aug 12 at 8:48
• What bends spacetime is not energy, but stress-energy-momentum (SE). The SE of a relativistic bullet (null dust) is zero, because its kinetic energy is frame dependent and its contribution to the SE is exactly canceled out by the opposite contribution of momentum (gravitomagnetism). Photons can be viewed as null dust with a zero SE tensor - light does not bend spacetime. So a kugelblitz made of light alone is impossible, the beams would just cross each other and move on. To make a black hole, you’d need a material target to convert the kinetic energy of photons into the energy of interactions. Commented Aug 13 at 5:26
• @safesphere kinetic eneregy of a system of two non-collinear photons is positive in any frame, you can't contribute any amount of momentum to cancel the inward or outward relative motion. Commented Aug 13 at 13:10
• @Ruslan It doesn’t matter. If each photon doesn’t curve spacetime, then any system of any number of them doesn’t either, because they don’t interact with each other. Commented Aug 13 at 15:57
• Another common misconception is “putting enough mass/energy within the Schwarzschild radius” to create a black hole. However, the radius of the Schwarzschild horizon defined as the spacelike radial distance to the origin is zero, as follows from the metric. Hence putting any mass/energy within any finite radius would not create a black hole until this matter goes into a gravitational collapse. Such a collapse however is not an option for photons, so again a kugelblitz made of light alone is impossible. Commented Aug 13 at 16:29

At high enough intensities light forms particle-antiparticle pairs which carry energy away from the region in which you're trying to form a black hole:

https://arxiv.org/abs/2405.02389

This constrains the size of the resulting black hole to less than $$10^{-29}m$$ or more than $$10^8m$$ in radius. For kugelblitzes larger than $$10^8m$$ this would require about $$10^{53}J$$ which is larger than the energy output from a bright quasar over 10,000 years. This is well beyond current technology and might be impossible.

• Glad to see one of my professors as an author to a cool paper like this. Commented Aug 12 at 9:07
• Nice disclaimer ;) Commented Aug 12 at 9:18
• I understand, but let's forget for a moment about quantum effects. In that paper they specifically say "we consider the scenario where an external flux of electromagnetic radiation is being focused on a spherical region until there is enough energy to form a Schwarzschild black hole", so they assume there is a steady influx of energy into the spherical region. My question is how that is even possible. Commented Aug 12 at 10:53
• @summer The relevant constraint is the amount of energy required, not producing light in an approximately spherical intensity distribution. If you want to understand focusing of laser beams see "Lasers" by Siegman Chapters 14-16. Then you could consider arranging some lasers shining through a spherical distribution of lenses so that their beam waists are centred at a point inside the sphere and a roughly spherical intensity distribution forms. If the lasers aren't mutually coherent you might not have to worry about interference effects. Commented Aug 12 at 18:31
• At high enough intensities light forms particle-antiparticle pairs” - This is not a fact, but only a hypothesis (with arguments against it). Self interaction of light in open space (away from matter) has not been observed. Commented Aug 14 at 0:11

It's always good to ball park things and figure out how your system scales with parameters. So just rando pulling 30,000 km (a huge blackhole) as a starting point...not good, esp when COTS lasers have 1 ns pulse widths.

So we have $$N$$ lasers with pulse width $$L$$ and total energy per pulse $$E_p$$.

We turn them into an inverse Dyson sphere of radius $$F$$ (for Freeman--since $$R$$ is taken).

So our setup can put

$$E = NE_p$$

into a volume:

$$V \approx 4 L^3$$

for an energy density:

$$u = \frac E V = \frac{NE_p}{4L^3}$$

From that, you can calculate the electric field and compare with the Schwinger Limit (https://en.wikipedia.org/wiki/Schwinger_limit), but I will proceed classically...

That energy has a mass

$$M = E/c^2$$

$$r = \frac L 2$$

which we're setting to the Schwarzschild radius:

$$r = r_s = \frac{2GM}{c^2} = \frac{2GNE_p}{c^4} = \frac L 2$$

which I can solve for the number of lasers:

$$N = \frac{c^4}{G}\frac{L}{4E_p}$$

So the last laser I worked with was a YAG with 1 joule in a 1 meter pulse:

$$N = 5 \times 10^{19}\,{\rm mol} = 80\, \mu{\rm mol^2}$$

That I can almost measure lasers in moles-squared is a concern.

Pick a spot size, I'll do:

$$a = 1\,{cm^2}$$

for a total area:

$$A = Na \approx 3 \times 10^{39}\,{\rm m^2}$$

$$F = \Big(\frac{A}{4\pi}\Big)^{\frac 1 2}$$

$$F \approx \frac 3 2 \times 10^{19}\,{\rm m} = 1640\,{ly}$$

so that's a real civil engineering project. The timing constraints alone, and since $$H_0 \approx 2\,{\rm cm/s/ly}$$, you have:

$$\dot F = 65\,{\rm m/s}$$

from the expanding universe.

Since we worked out the formula, you can pick a different laser set up and do better. Calling the beam width $$d$$:

$$F \propto d\sqrt{\frac L {E_p}}$$

(which triggers my sanity check--I have length to the 3/2...is that covered by root $$G/c^4$$?...I think so).

So a femto second laser gets $$2F$$ down to 3 light years.

A google search of "most powerful laser in the world" is frustratingly unscientific, but I see a peta-watt, so that's another factor of 1000, and lets do a 1mm spot size for another factor of 10:

$$F = 1.5\,{\rm Tm} \approx 10\,{\rm A.U.}$$

which is a solar system scale project..much easier. (Though that trigger another sanity check...10 AU is 80 light minutes..there's 8760 hours in a year...no that's good, I had a factor of 10K).

Note that if the laser efficiency fails:

$$\epsilon \gt \frac L F$$

then the energy to run the inverse Dyson sphere will form a horizon.