Merger transitions in brane–black-hole systems: Criticality, scaling, and self-similarity

We propose a toy model for studying merger transitions in a curved spacetime with an arbitrary number of dimensions. This model includes a bulk $N$-dimensional static spherically symmetric black hole and a test $D$-dimensional brane ($D\le N-1$) interacting with the black hole. The brane is asymptotically flat and allows a $O(D-1)$ group of symmetry. Such a brane–black-hole (BBH) system has two different phases. The first one is formed by solutions describing a brane crossing the horizon of the bulk black hole. In this case the internal induced geometry of the brane describes a $D$-dimensional black hole. The other phase consists of solutions for branes which do not intersect the horizon, and the induced geometry does not have a horizon. We study a critical solution at the threshold of the brane–black-hole formation, and the solutions which are close to it. In particular, we demonstrate that there exists a striking similarity of the merger transition, during which the phase of the BBH system is changed, both with the Choptuik critical collapse and with the merger transitions in the higher dimensional caged black-hole–black-string system.