It has been known since the 1980′s that black strings are unstable to long wavelength perturbations. However, it is difficult to establish what the end point of this instability is. Similarly, it is expected that for Kaluza-Klein black holes – e.g. where one spacetime dimension is wrapped around a circle – that there would be a phase transition between localized black holes and black strings as the size of the compact dimension is decreased. Lorenzo Sorbo, Jennie Traschen and I tried to study this transition in a dynamical setting by employing the “Kastor-Traschen” space times. These are multi-black hole solutions in a deSitter background.
We considered a one-dimensional array of such black holes, which is equivalent to wrapping one dimension on a circle, in the collapsing phase of deSitter. We studied the evolution of black hole and deSitter apparent horizons. We expected to find that as the universe shrank that the black hole horizons would merge into a black string.
However, we found instead that the black hole horizons stay separate, which turned out to be a good thing. There turns out to be no non-singular charged deSitter black string for them to merge into. The actual outcome is then in accordance with cosmic censorship. We call this the “Clayton Effect” – after the Clayton Antitrust act which prohibits mergers that are antithetical to the public good!
Link to paper