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2013

The Einstein-Klein-Gordon-AdS system for general boundary conditions

Holzegel, Gustav H., Warnick, Claude M.

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We construct unique local solutions for the spherically-symmetric Einstein-Klein-Gordon-AdS system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence.

The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass.
For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes.
The present paper furnishes a starting point for such global investigations.

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P. Breitenlohner and D. Z. Freedman, “Stability in gauged extended supergravity,” Annals Phys
1982
Earlier work this paper cites.
D. Christodoulou, “The Problem of a Selfgravitating Scalar Field,” Commun. Math. Phys
1986
Earlier work this paper cites.
H. Friedrich, “Einstein equations and conformal structure – Existence of anti de Sitter type space-times,” J.Geom.Phys
1995
Earlier work this paper cites.
C. Martinez, R. Troncoso, and J. Zanelli, “Exact black hole solution with a minimally coupled scalar field,” Phys.Rev
2004
Earlier work this paper cites.
T. Hertog and K. Maeda, “Black holes with scalar hair and asymptotics in N = 8 supergravity,” JHEP
2004
Earlier work this paper cites.
T. Hertog and G. T. Horowitz, “Designer gravity and field theory effective potentials,” Phys.Rev.Lett
2005
Earlier work this paper cites.
H. Ringstroem, “Future Stability of the Einstein-non-linear scalar field system,” Invent. math
2008
Earlier work this paper cites.

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