In hot pursuit of a stable wormhole in beyond Horndeski theory

TL;DR

This paper analyzes the linear stability of static, spherically symmetric wormholes in beyond Horndeski scalar-tensor theories, deriving comprehensive conditions to ensure the absence of high-energy instabilities and providing an example solution.

Contribution

It extends existing stability criteria for wormholes in beyond Horndeski theories by including high energy mode constraints and offers an explicit example satisfying all these conditions.

Findings

Derived new stability conditions for high energy modes.

Extended the stability analysis to include both parity sectors.

Provided an explicit wormhole solution meeting all stability criteria.

Abstract

We consider the issue of stability at the linearized level for static, spherically symmetric wormhole solutions within a subclass of scalar-tensor theories of beyond Horndeski type. In this class of theories we derive a set of stability conditions ensuring the absence of ghosts and both radial and angular gradient instabilities about a static, spherically-symmetric background. This set of constraints extends the existing one and completes the stability analysis for high energy modes in both parity odd and parity even sectors, while "slow" tachyonic instabilities remain unconstrained. We give an example of beyond Horndeski Lagrangian admitting a wormhole solution which complies with all stability constraints for the high energy modes.