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2014

On the nonlinear instability of confined geometries

Okawa, Hirotada, Cardoso, Vitor, Pani, Paolo

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The discovery of a "weakly-turbulent" instability of anti-de Sitter spacetime supports the idea that confined fluctuations eventually collapse to black holes and suggests that similar phenomena might be possible in asymptotically-flat spacetime, for example in the context of spherically symmetric oscillations of stars or nonradial pulsations of ultracompact objects.

Here we present a detailed study of the evolution of the Einstein-Klein-Gordon system in a cavity, with different types of deformations of the spectrum, including a mass term for the scalar and Neumann conditions at the boundary.
We provide numerical evidence that gravitational collapse always occurs, at least for amplitudes that are three orders of magnitude smaller than Choptuik's critical value and corresponding to more than $10^5$ reflections before collapse.
The collapse time scales as the inverse square of the initial amplitude in the small-amplitude limit.

On the nonlinear instability of confined geometries · Around

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Nuovo Cim. B44S10
W. Israel, · 1966
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Phys.Rev.Lett. 70
M. W. Choptuik, · 1993
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The global nonlinear stability of the Minkowski space
D. Christodoulou and S. Klainerman, · 1993
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Lorentzian wormholes: From Einstein to Hawking
M. Visser, · 1995
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Int.J.Mod.Phys. D10
M. Alcubierre et al · 2001
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