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

TL;DR

This paper analyzes a family of Lorentzian wormholes, exploring their geometry, matter content, scalar quasinormal modes, and echoes, highlighting their potential as models for exotic compact objects in gravitational wave physics.

Contribution

It provides a detailed analysis of scalar quasinormal modes and echoes in a family of wormholes, linking geometric parameters to wave behavior and energy conditions.

Findings

Effective potential can have double barrier features.

Quasinormal modes vary with wormhole parameters.

Echoes appear for large metric parameter n.

Abstract

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). Subsequently, using numerous methods, we obtain the scalar quasinormal modes (QNMs). We note the behaviour of the QNMs as a function of $n$ (the metric parameter) and $b_0$ (the wormhole throat radius). Thus, the shapes and sizes of the wormholes, governed by the metric parameter $n$ and the throat radius $b_0$ are linked to the variation and the values of the QNMs. Finally, we demonstrate how, for large $n$, the time domain profiles exhibit, expectedly, the occurence of echoes. In summary, our results suggest that this family of wormholes may indeed be used as a template for further studies on the gravitational wave physics of exotic compact objects.