The Gravitational Perturbation of a Morris-Thorne Wormhole and The Newman-Penrose Formalism

TL;DR

This paper derives the gravitational perturbation equations for a Morris-Thorne wormhole using the Newman-Penrose formalism, focusing on a specific dust matter perturbation modeled by a Gaussian pulse.

Contribution

It applies the Newman-Penrose formalism and Teukolsky equation to analyze wormhole perturbations, providing a new approach to studying their stability and response.

Findings

Derived the master equation for Weyl scalar perturbations

Decomposed perturbations into spin-weighted spherical harmonics

Analyzed the effect of a Gaussian dust pulse on the wormhole

Abstract

The gravitational perturbation of the Morris-Thorne wormhole has been derived by using the Newman-Penrose formalism. We apply Teukolsky equation to the wormhole spacetime, compute the perturbed Weyl scalars, $\Psi_{4}^{(1)}$ and obtain its master equation, decomposed in spin weighted spherical harmonics with spin weight $-2$. For simplicity, we consider the perturbation provoked by a single gaussian pulse of pressureless dust matter.