Can light be somehow confined to create a kugelblitz?

Question

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?

Answer 1

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.

Answer 2

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

$$ M = E/c^2 $$

in a radius:

$$ r = \frac L 2 $$

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:

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

solving for the radius:

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

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

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.