Stability in Designer Gravity

TL;DR

This paper investigates the stability of designer gravity theories with tachyonic scalars in AdS space, establishing energy bounds and conditions for stable ground states, and explores implications for higher dimensions.

Contribution

It constructs Hamiltonian generators for asymptotic symmetries in designer gravity and proves stability conditions related to the boundary function W.

Findings

Positivity of spinor charge bounds the energy from below.

Stable ground states correspond to solutions with W's global minimum.

Minimum energy solutions are shown to be static.

Abstract

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.