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

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.

arXiv comment20 pages. Revised version

References in corpus (11)

• Stability of phantom wormholes
• Instabilities of wormholes and regular black holes supported by a phantom scalar field
• Fate of the first traversible wormhole: black-hole collapse or inflationary expansion
• Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis
• Example of a stable wormhole in general relativity
• Scalar and axial quasinormal modes of massive static phantom wormholes
• Rotating Scalar Field Wormhole
• On the linear instability of the Ellis-Bronnikov-Morris-Thorne wormhole
• Ring Wormholes in D-Dimensional Einstein and Dilaton Gravity
• Wormhole solutions with a complex ghost scalar field and their instability
• Gauge-invariant spherical linear perturbations of wormholes in Einstein gravity minimally coupled to a self-interacting phantom scalar field

Cited by in corpus (6)

• Ellis Wormholes in Anti-De Sitter Space
• Stable soliton dark matter wormhole in non-minimally coupled $f(\mathcal{Q},\mathcal{T})$ gravity
• Novel triple barrier potential for axial gravitational perturbations of a family of Lorentzian wormholes
• Formation of Bound States of scalar fields in AdS-asymptotic Wormholes
• Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions
• Geodesic completeness of effective null geodesics in regular space-times with non-linear electrodynamics