Stability in Designer Gravity

Details Stability in Designer Gravity Stability in Designer Gravity

2005-08-24

arxiv.org/abs/hep-th/0508181v2

Class.Quant.Grav. 22 (2005) 5323-5342

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

10.1088/0264-9381/22/24/007

We study the stability of designer gravity theories, in which one considers gravity coupled to a tachyonic scalar with anti-de Sitter boundary conditions defined by a smooth function W. We construct Hamiltonian generators of the asymptotic symmetries using the covariant phase space method of Wald et al.and find they differ from the spinor charges except when W=0. The positivity of the spinor charge is used to establish a lower bound on the conserved energy of any solution that satisfies boundary conditions for which $W$ has a global minimum. A large class of designer gravity theories therefore have a stable ground state, which the AdS/CFT correspondence indicates should be the lowest energy soliton. We make progress towards proving this, by showing that minimum energy solutions are static. The generalization of our results to designer gravity theories in higher dimensions involving several tachyonic scalars is discussed.

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