Stability in Designer Gravity
Thomas Hertog, Stefan Hollands
TL;DR
The paper studies stability in designer gravity theories in AdS, where a tachyonic scalar obeys boundary conditions defined by a function $W(\alpha)$. Using the covariant phase space formalism, the authors derive Hamiltonian charges for asymptotic symmetries and relate them to spinor charges, establishing a lower bound on the conserved energy whenever $W$ has a global minimum. They show that minimal-energy configurations are static under certain conditions and discuss the role of lowest-energy solitons as ground states, with AdS/CFT providing a complementary perspective on vacua. The results extend to higher dimensions with multiple scalars and outline generalizations, offering a robust gravitational basis for energy stability in a broad class of boundary conditions. Overall, the work connects gravitational stability in designer gravity to dual field theory expectations and motivates numerical and higher-dimensional investigations to fully characterize ground states.
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.