Revisiting a family of wormholes: geometry, matter, scalar quasinormal modes and echoes

Understand

We revisit a family of ultra-static Lorentzian wormholes which includes Ellis-Bronnikov spacetime as a special case.

• We first show how the required total matter stress energy (which violates the local energy conditions) may be split into a part due to a phantom scalar and another extra piece (which vanishes for Ellis--Bronnikov) satisfying the Averaged Null Energy Condition (ANEC) along radial null geodesics.
• Thereafter,we examine the effective potential for scalar wave propagation in a general setting.
• Conditions on the metric function, for which the effective potential may have double barrier features are written down and illustrated (using this class of wormholes).