Stable phantom-energy wormholes admitting conformal motions

TL;DR

This paper constructs stable wormhole solutions with phantom energy by assuming conformal symmetry, showing stability under linear radial perturbations for specific equation of state parameters.

Contribution

It demonstrates that wormholes with phantom energy and conformal motions can be stable, extending previous work by explicitly analyzing stability conditions.

Findings

Wormholes with $p=\omega\rho$ admit conformal motions.

Stability is achieved for $-1.5<\omega<-1$ under radial perturbations.

The solutions support phantom energy as a viable matter source for stable wormholes.

Abstract

It has been argued that wormholes are as good a prediction of Einstein's theory as black holes but the theoretical construction requires a reverse strategy, specifying the desired geometric properties of the wormhole and leaving open the determination of the stress-energy tensor. We begin by confirming an earlier result by the author showing that a complete wormhole solution can be obtained by adopting the equation of state $p=\omega\rho$ and assuming that the wormhole admits a one-parameter group of conformal motions. The main purpose of this paper is to use the assumption of conformal symmetry to show that the wormhole is stable to linearized radial perturbations whenever $-1.5<\omega <-1$.