Domain wall interacting with a black hole: A new example of critical phenomena

We study a simple system that comprises all the main features of critical gravitational collapse, originally discovered by Choptuik and discussed in many subsequent publications. These features include universality of phenomena, mass-scaling relations, self-similarity, symmetry between supercritical and subcritical solutions, etc. The system we consider is a stationary membrane (representing a domain wall) in a static gravitational field of a black hole. For a membrane that spreads to infinity, the induced (2+1)-dimensional geometry is asymptotically flat. In addition to solutions with Minkowski topology there exist also solutions with the induced metric and topology of a (2+1)-dimensional black hole. By changing boundary conditions at infinity one finds that there is a transition between these two families. This transition is critical and it possesses all the above-mentioned properties of critical gravitational collapse. It is remarkable that the characteristics of this transition can be obtained analytically. In particular, we find exact analytical expressions for scaling exponents and wiggle periods. Our results indicate that critical phenomena in black hole physics are more widespread than might have been expected.