Time-periodic solutions of massive scalar fields in AdS background: perturbative constructions

TL;DR

This paper develops perturbative methods to construct time-periodic solutions of massive scalar fields coupled to Einstein gravity with negative cosmological constant, analyzing stability and including examples from supergravity.

Contribution

It introduces a perturbative approach to find periodic solutions for scalar fields in AdS backgrounds, including self-interacting models from supergravity.

Findings

Critical amplitude increases for less massive fields.

Constructed explicit examples including supergravity truncations.

Analyzed stability of solutions across dimensions.

Abstract

We consider scalar fields which are coupled to Einstein gravity with a negative cosmological constant, and construct periodic solutions perturbatively. In particular, we study tachyonic scalar fields whose mass is at or above the Breitenlohner-Freedman bound in four, five, and seven spacetime dimensions. The critical amplitude of the leading order perturbation, for which the perturbative expansion breaks down, increases as we consider less massive fields. We present various examples including a model with a self-interacting scalar field which is derived from a consistent truncation of IIB supergravity.