Two worlds collide: Interacting shells in AdS spacetime and chaos

Abstract

We study the simplest two-body problem in asymptotically anti-de Sitter spacetime: two, infinitely thin, concentric spherical shells of matter. We include only gravitational interaction between the two shells, but we show that the dynamics of this system is highly nontrivial. We observe prompt collapse to a black hole, delayed collapse and even perpetual oscillatory motion, depending on the initial location of the shells (or their energy content). The system exhibits critical behavior, and we show strong hints that it is also chaotic.

Comments: 8 pages, 7 figures; v2: updated references and added short discussion on the Lyapunov exponent; v3: matches published version