New simulations of head-on collisions of particles travelling at nearly the speed of light show that black-hole formation can occur at lower collision energies than expected, according to a team of researchers in the US. The researchers attribute this to a “gravitational focusing effect” whereby the two colliding particles act like gravitational lenses, focusing the energy of the collision into two distinct light-trapping regions that eventually collapse into a single black hole. Although the work shows that black holes can form at lower collision energies than expected, the team says that the result has no impact on real particle collisions taking place at the Large Hadron Collider (LHC) at CERN.

From 2008 onwards, when the LHC was first scheduled to be switched on, there were rumours about what the experiment might create – extra dimensions, sparticles and strangelets, vacuum bubbles and, of course, planet-destroying black holes. Although the experiment ran seamlessly from November 2009 for more than two years and scientists found no evidence whatsoever for the formation of micro black holes, the fascination with black-hole formation and evaporation continues – among researchers and the media.

Planck scales and beyond

Frans Pretorius and William East of Princeton University in the US want to better understand the dynamics of particle collisions at the super-Planck scale.

Planck units are a system of units comprised of the simplest algebraic combinations of the fundamental constants of nature – the speed of light c, Newton’s constant G, Planck’s constant h and so on. For example, a combination of the constants to form a unit of Planck energy (E_p) is about 2 × 10⁹ J. Pretorius explains that a super-Planck-scale collision is a collision between two fundamental particles where the total energy (rest energy (E_r) plus the kinetic energy) exceeds E_p. At the Planck scale, quantum-gravity effects are expected to start playing a role in the interaction. However, at energies greater than E_p (and no-one knows exactly how much greater), classical gravity dominates the interaction.

So the researchers wanted a completely classical calculation, and this, explains Pretorius, is the “crucial ingredient in the argument that super-Planck-scale collisions form black holes, regardless of any non-gravitational interactions between the particles”. He goes on to explain that this is important, as currently we do not know exactly what quantum-gravity interactions occur at the Planck scale. According to Pretorius, the new results suggest that for energies sufficiently above the Planck scale it does not matter – a black hole will form around the interaction, hiding all quantum effects, at least temporarily.

Critical energies

While considering the super-Planck-scale regime, the researchers look at specific “gamma” (γ) values in the collisions. Pretorius explains to physicsworld.com that γ is a measure of the kinetic energy of the interaction; that is, if the rest energy of one of the colliding particles of mass m is E_r = mc², then the total energy of the particle in motion is E_t = γ × E_r. So, when two particles of mass m collide, each moving with velocity v towards each other in the reference frame of the lab, the total energy of the collision is 2 × γ × E_r.

According to the researchers, the critical γ depends on the particular model of a particle, and in their simulations, the particles of choice are “fluid stars” – a hypothetical and perfect “star” or particle that Pretorius describes as a “classical model of a fermionic star”. They used the fluid star because its γ value is high enough that the total collision energy would allow for a black hole to form. “Since our calculation is purely classical, so no h, this serves as the proxy of the Planck energy,” says Pretorius.

A previous estimate for black-hole formation – known as the “Hoop Conjecture” and developed by Kip Thorne in 1994 – says that an object compressed in a highly spherical manner will “form a black hole around itself when and only when its circumference in all directions becomes less than the critical circumference”. This “critical circumference” is directly related to the Schwarzschild radius (r_s) of the object. But in the case of their collisions with super-Planck-scale fluid stars, Pretorius and East found that black-hole formation “actually begins at a fraction of about one-third of this [Hoop Conjecture estimate] energy”.

Simulating colliding stars

In terms of the actual simulations, the researchers begin with the two model particles – the fluid stars – moving towards each other at high velocity. When they first collide, they are in a sense at such high velocities that the particles just smash through each other. “However, the gravitational field of each is so strong because of the extra energy coming from the large gammas, that the gravitational force, which is attractive, strongly focuses each particle towards the collision axis,” says Pretorius. The “fluid” material compresses because of this focusing, and eventually by so much that each particle collapses to form a black hole. “We measure this in the simulation by the apparent horizons, which baring technical details are essentially the event horizons of the black holes. These initially two separate horizons then merge to form a larger black hole,” he says.

You can see the simulations here – the first video is for γ = 8, which is strong enough to produce some lensing but not enough to form any black holes. The second is for γ = 10 and the black holes are formed.

Black-hole death?

Pretorius and East are clear that their simulation results have no real bearing on safety issues at any high-energy experiments. They say that even if such black holes are formed, they would still be completely benign given what we know about them. According to the team, the results might give researchers a better idea of the energies at which black holes might start to form. “Though the key question is what the true Planck scale is,” muses Pretorius. The units he mentioned above suggest that the Planck energy is 10¹⁶ TeV in LHC-like terms, so about 15 orders of magnitude above LHC energies. If this is the case, it is not even remotely possible for the LHC to form black holes, even with the factor of one-third decrease in the threshold energy. “However, if there are extra, small dimensions, as string theory predicts, then the true Planck scale could be lower. There are no firm predictions on how much lower, so this is a highly speculative scenario. If black holes were formed, it would strongly indicate that there are extra dimensions, which would be a very profound discovery,” says Pretorius.

The research is published in Physical Review Letters.