How to tell the shape of a wormhole by its quasinormal modes

TL;DR

This paper demonstrates how to reconstruct the shape of a spherically symmetric traversable wormhole near its throat using high-frequency quasinormal modes, providing a method to infer spacetime geometry from observable oscillation data.

Contribution

It introduces a unique inverse method to determine wormhole shape functions from quasinormal modes, applicable to certain classes of wormholes, using a WKB fitting approach.

Findings

Reproduces near-throat geometries of Bronnikov-Ellis and Morris-Thorne wormholes.

Shows the inverse problem solution is unique for some wormhole classes.

Validates the method with high multipole number quasinormal modes.

Abstract

Here we shall show how to reconstruct the shape function of a spherically symmetric traversable Lorenzian wormhole near its throat if one knows high frequency quasinormal modes of the wormhole. The wormhole spacetime is given by the Morris-Thorne ansatz. The solution to the inverse problem via fitting of the parameters within the WKB approach is unique for arbitrary tideless wormholes and some wormholes with non-zero tidal effects, but this is not so for arbitrary wormholes. As examples, we reproduce the near throat geometries of the Bronnikov-Ellis and tideless Morris-Thorne metrics by their quasinormal modes at high multipole numbers $\ell$.