Gravitational perturbations in the Newman-Penrose formalism: Applications to wormholes

TL;DR

This paper investigates the linear stability of gravitational perturbations in spherically symmetric wormholes using the Newman-Penrose formalism, deriving a master equation and demonstrating the absence of unstable modes.

Contribution

It introduces a Newman-Penrose-based method to analyze gravitational perturbations in wormholes and derives a master equation for odd-parity perturbations.

Findings

No unstable vibrational modes found in studied wormholes.

Master equation successfully describes gravitational perturbations.

Method applicable to various wormhole geometries.

Abstract

In this work we study the problem of linear stability of gravitational perturbations in stationary and spherically symmetric wormholes. For this purpose, we employ the Newman-Penrose formalism which is well-suited for treating gravitational radiation in General Relativity, as well as the geometrical aspect of this theory. With this method we obtain a "master equation" that describes the behavior of gravitational perturbations that are of odd-parity in the Regge-Wheeler gauge. This equation is later applied to a specific class of Morris-Thorne wormholes and also to the metric of an asymptotically flat scalar field wormhole. The analysis of the equations that these space-times yield reveals that there are no unstable vibrational modes generated by the type of perturbations here studied.