Polar modes and isospectrality of Ellis-Bronnikov wormholes

TL;DR

This paper analyzes the polar perturbations of Ellis-Bronnikov wormholes, revealing isospectrality in massless cases and identifying distinct quasinormal mode branches in massive cases, with detailed frequency calculations.

Contribution

It derives coupled perturbation equations for Ellis-Bronnikov wormholes and uncovers isospectrality and mode branch structures, extending understanding of wormhole stability and oscillations.

Findings

Massless wormholes exhibit isospectrality with axial modes.

Finite mass wormholes have two distinct polar mode branches.

Calculated quasinormal mode frequencies for l=2,3,4.

Abstract

We consider polar perturbations of static Ellis-Bronnikov wormholes and derive the coupled set of perturbation equations for the gravitational and the scalar field. For massless wormholes the perturbations decouple, and we obtain two identical master equations for the scalar and gravitational modes, which moreover agree with the master equation for the axial modes. Consequently there is isospectrality with threefold degenerate modes. For a finite mass of the background wormhole solutions, the equations are coupled. We then obtain two distinct branches of polar quasinormal modes for a given multipole number l, associated with the presence of the two types of fields. We calculate the quasi-normal mode frequencies and decay rates for the branches with l=2, 3 and 4. For a given l the real frequencies of the two branchesget the closer, the higher the multipole number gets.