Wave length constraint in “black-hole” jet breakup
In last week’s colloquium, the speaker talked about the black hole merge simulation. At the end, he roughly mentioned that if there exists an extra 5th dimension, the black hole can break up in higher dimensions…(I may misunderstand this part, so correct me please). Simulation shows that a jet (cylinder) of black hole with the axis direction along the extra dimension is non-stable and breaks up into self-similar cascading beads. Although the real break up may not be possible because the cosmic sensor prohibits naked singularities and thus topological change of black hole, but the dynamics is pretty much like a rayleigh-plateau instability in liquid jet. The latter can be observed in your daily life as you open the tap and let the water run down. You will notice that with some condition, the jet will break up into beads. However, when black hole is concerned, there is a fundamental difference as I think. The water jet breaks up because the beads possess less surface energy comparing to cylinder. However, for black hole, since the entropy is proportional to the surface area, thus the beads should retain larger surface area comparing to the cylinder. I did a simple calculation by assuming that a cylinder (height h and radius r) breaks up into N identical spheres ( or circles in 2D, so the wave length \lambda is about h/N ) and calculate the surface area in both cylinder and beads cases, then compare the results. The result shows that for liquid, roughly speaking, to reduce surface area, we require r/ \lambda < 1; while for black hole, we need r/\lambda > 1. To conclude, in water breakup, long wave length is preferred; in black hole and in higher dimensions, short wave length is preferred.
