Geons and Spin-2 Condensates in the AdS Soliton

TL;DR

This paper investigates the formation of spin-2 condensates in the AdS soliton background by constructing geons from gravitational perturbations, exploring their potential to model d-wave superconductors, but finds no phase transition due to higher free energy.

Contribution

It introduces a method to construct geons from gravitational perturbations of the AdS soliton and examines their role in modeling d-wave superconductivity.

Findings

Charged spin-2 condensate forms but has higher free energy.

No phase transition occurs to the spin-2 condensate state.

Geons can be constructed from gravitational perturbations in the AdS soliton.

Abstract

We construct geons starting with gravitational perturbations of the AdS soliton. Previous studies of a charged scalar field in the soliton background showed a holographic insulator/superconductor transition at a critical chemical potential. We explore the possibility that dimensional reduction of the geon could model a transition to a d-wave superconductor. We find that although one does get a charged spin-2 condensate, it has higher free energy than the state without the condensate, so there is no phase transition.