Title: No black holes from light
Authors: Alvaro Alvarez-Dominguez, Luis J. Garay, Eduardo Martin-Martinez, and Jose Polo-Gomez
First Author’s Institution: Departamento de Fisica Teorica and IPARCOS, Universidad Complutense de Madrid
Status: Published in PRL [closed access]
Theoretically, any force carrying enough energy could warp the fabric of space-time so much that it creates a singularity. We know that gravity is capable of this: as gravity pulls immense amounts of matter together, it creates a warp so strong it creates a black hole. Gravity, as opposed to the other three fundamental forces (strong, weak, and electromagnetic), is kind of set up better to do this. It is weaker, but it is effective on much larger scales, which means a heavy neutron star can drag a neutron star that’s relatively far away to collide with it and create a black hole. The strong and the weak nuclear forces are stronger than gravity, but they only work on incredibly small scales (i.e. the length of an atomic nucleus). However, the electromagnetic force (carried by light) is strong, and it has an infinite reach, the same as gravity. Thus, ever since Einstein theorised it in his theory of general relativity, scientists have wondered if light can create enough energy to form a singularity in the way gravity does.
This phenomenon has been dubbed a kugelblitz by physicists–German for “ball lightning.” It is allowed as a solution to the Einstein-Maxwell equations, but most works exploring its theoretical existence haven’t explored whether quantum mechanics would actually allow one to form. This is where the authors of today’s paper pick up, and investigate whether you can actually concentrate enough light energy in a small distance to make it collapse in on itself.
Quantum Mechanical Party-Pooper
The major inhibitor to the formation of a kugelblitz, these authors argue, is the phenomenon of particle-antiparticle creation. For a kugelblitz to form, it would require an incredible amount of energy from the electromagnetic field. Unfortunately, at these field strengths, you run into the issue that particle and antiparticle pairs will be created (this is also commonly known as “pair production”). Strong enough electromagnetic fields creating matter is an effect that has been studied in depth, referred to as the Schwinger effect. It has never been observed in the laboratory because the field strengths required (1018 Volts/meter) have never been reached.
But how can the creation of particles and antiparticles inhibit the formation of a kugelblitz? To put it simply, as energy transitions to matter via pair production, the particles created within the region could then travel outside of the region, taking their energy with them. At the end of the process, the electromagnetic field has decreased in energy. If enough of these pairs are created, it could reduce the amount of energy to such a degree that a black hole could no longer form.
The authors set up the scenario as a spherical influx of electromagnetic energy (aka light) concentrated on a single point in space. As we now know, the energy is taken out of the sphere as electron-positron pairs are produced and some travel away. This creates a change of energy that can be described by the rate that the EM energy is coming in, minus the energy that the pair production takes out. The energy that the pair production takes out is difficult to estimate, since the Schwinger effect has never actually been measured. They calculate this “dissipation rate” by modeling the energy carried away by a theoretical particle as an adiabatic pulse that leaves the sphere in some characteristic time. This gives them a rough mathematical formulation for the dissipation rate as a function of time.
Kugelblitz vs. Reality
When they compare this dissipation rate to the energy that is going into the sphere, they are able to find the constraints of how much energy one would need to form a kugelblitz ~ roughly 1027 Volts / the radius of the original sphere. To create a kugelblitz with about a ~1m radius, you’d need a laser pulse of 1083 Watts/m2. The best laser pulse we have now is a measly 1027 Watts/m2 in comparison, so it’s unlikely we’ll be able to create our own black hole in the lab (way to crush my hopes and dreams…).
But what about space? It’s not looking too promising out there either: the intensity required for a kugelblitz to form is much higher than our highest-recorded energy sources like quasars or supernovae. Luckily we still don’t really know what the highest mass limit is for a star, so maybe there’s a 500 solar mass star out there just waiting to go uber-hypernova.
All this said, there are many caveats to their calculations. For one, the theoretical formation they describe requires light to be coming in from all directions, focused on one single point. This doesn’t really happen in space, at least as far as we’re aware. And moreover, (an astronomer’s favourite question) what about the magnetic field? The authors include these caveats in their discussion and it is clear there is much more that work can be done to really test the extremes of these measurements. If you’re hoping for a kugelblitz, the odds aren’t looking too good, but in a vast expanse of the universe you can never really rule something out for certain.
Astrobite edited by Cole Meldorf
Featured Image Credit: Wikimedia Commons
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