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.

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

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Cited by in corpus (14)

• Junction conditions and thin-shells in perfect-fluid $f\left(R,T\right)$ gravity
• Double gravitational layer traversable wormholes in hybrid metric-Palatini gravity
• Gravitational geons in asymptotically anti-de Sitter spacetimes
• Existence and stability of relativistic fluid spheres supported by thin shells
• Black Hole Formation in AdS Einstein-Gauss-Bonnet Gravity
• Junction conditions in gravity theories with extra scalar degrees of freedom
• The instability of anti-de Sitter space-time
• Oscillating Shells and Oscillating Balls in AdS
• Gravitational systems in asymptotically anti-de Sitter space-times
• High energy collision without fine tuning: Acceleration and multiple collisions of shells in a bound system
• Phase Diagram of Stability for Massive Scalars in Anti-de Sitter Spacetime
• Repeated crossing of two concentric spherical thin-shells with charge
• Cosmological and astrophysical applications of modified theories of gravity
• Energy transfer in the collision of two scalar wave packets in spherical symmetry