Adiabatic pumping solutions in global AdS

TL;DR

This paper constructs and analyzes a family of stationary solutions in global AdS with a scalar field, exploring their stability, nonlinear dynamics, and relation to time-periodic solutions and other known backgrounds.

Contribution

It introduces a new class of pumping solutions in AdS, studies their stability, and constructs non-stationary time-periodic solutions, advancing understanding of scalar field dynamics in AdS.

Findings

Pumping solutions are regular, often have negative mass.

Both stable and unstable branches are identified.

Unstable solutions can decay to black holes or limit cycles.

Abstract

We construct a family of very simple stationary solutions to gravity coupled to a massless scalar field in global AdS. They involve a constantly rising source for the scalar field at the boundary and thereby we name them pumping solutions. We construct them numerically in $D=4$. They are regular and, generically, have negative mass. We perform a study of linear and nonlinear stability and find both stable and unstable branches. In the latter case, solutions belonging to different sub-branches can either decay to black holes or to limiting cycles. This observation motivates the search for non-stationary exactly time-periodic solutions which we actually construct. We clarify the role of pumping solutions in the context of quasistatic adiabatic quenches. In $D=3$ the pumping solutions can be related to other previously known solutions, like magnetic or translationally-breaking backgrounds. From this we derive an analytic expression.