In hot pursuit of a stable wormhole in beyond Horndeski theory

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.