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2012

Nonlinear Collapse in the Semilinear Wave Equation in AdS

Liebling, Steven L.

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Previous studies of the semilinear wave equation in Minkowski space have shown a type of critical behavior in which large initial data collapse to singularity formation due to nonlinearities while small initial data does not.

Numerical solutions in spherically symmetric Anti-de Sitter (AdS) are presented here which suggest that, in contrast, even small initial data collapse eventually.
Such behavior appears analogous to the recent result of Ref.
[1] that found that even weak, scalar initial data collapse gravitationally to black hole formation via a weakly turbulent instability.

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N. Szpak, “Relaxation to Intermediate Attractors in Nonlinear Wave Equations,” Theoretical and Mathematical Physics
2001
Earlier work this paper cites.
P. Bizoń, T. Chmaj, and Z. Tabor, “On blowup for semilinear wave equations with a focusing nonlinearity,” Nonlinearity
2004
Earlier work this paper cites.
S. L. Liebling, “Threshold of singularity formation in the semilinear wave equation,” Phys.Rev
2005
Earlier work this paper cites.

Similar

P. Bizoń and A. Rostworowski, “On weakly turbulent instability of anti-de Sitter space,” Phys.Rev.Lett
Original
2011
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J. Jalmuzna, A. Rostworowski, and P. Bizoń, “A Comment on AdS collapse of a scalar field in higher dimensions,” Phys.Rev
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2011
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A. Buchel, L. Lehner, and S. L. Liebling, “Scalar Collapse in AdS,” Phys. Rev. D
Original
2012
Cited alongside, same era.

Then

A. Buchel, S. L. Liebling, and L. Lehner, “Boson stars in AdS,” in preparation
2012
Closest in time.
O. J. Dias, G. T. Horowitz, D. Marolf, and J. E. Santos, “On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions,” Class.Quant.Grav
Original
2012
Closest in time.

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