Traversable Wormholes Supported by Conformally Coupled Scalar Fields in D ≥ 4: Geometry, Geodesics, and Quasinormal Modes
Abstract
In this work, we analyze a two-parameter $(μ, b)$ asymmetric family of traversable wormhole solutions generated by a massless conformally coupled scalar field. We show that, for a suitable range of parameters, the spacetime is everywhere regular and has two asymptotically flat regions. We then define the wormhole throat and verify the flare-out condition, which leads to violations of the classical energy conditions in GR, thereby requiring exotic matter to hold the throat open. We further analyze the motion of photons governed by null geodesics through an effective potential. The resulting trajectories are computed numerically and visualized using embedding diagrams. Following this route, we investigate scalar perturbations governed by the massless Klein-Gordon equation and find the QNM spectrum semianalytically and numerically. Interestingly enough, we show that such perturbations are governed by only one parameter μ. Therefore, in D = 4, we find an isospectrality between the wormhole and the BBMB/Extremal Reissner-Nordström black hole. In the spirit of the seminal work of Morris and Thorne, we derive the conditions for traversability and compute the proper time for a traveler to traverse the wormhole. Finally, we discuss possible extensions and future directions for our work.
Related
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BibTeX
@misc{vidal2026traversable,
title = {{Traversable Wormholes Supported by Conformally Coupled Scalar Fields in $D \geq 4$: Geometry, Geodesics, and Quasinormal Modes}},
author = {Pablo Vidal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38217},
eprint = {2609.38217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38217},
}
RIS
TY - UNPB
TI - Traversable Wormholes Supported by Conformally Coupled Scalar Fields in D ≥ 4: Geometry, Geodesics, and Quasinormal Modes
AU - Pablo Vidal
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.38217
UR - https://arxiv.org/abs/2609.38217
AB - In this work, we analyze a two-parameter $(μ, b)$ asymmetric family of traversable wormhole solutions generated by a massless conformally coupled scalar field. We show that, for a suitable range of parameters, the spacetime is everywhere regular and has two asymptotically flat regions. We then define the wormhole throat and verify the flare-out condition, which leads to violations of the classical energy conditions in GR, thereby requiring exotic matter to hold the throat open. We further analyze the motion of photons governed by null geodesics through an effective potential. The resulting trajectories are computed numerically and visualized using embedding diagrams. Following this route, we investigate scalar perturbations governed by the massless Klein-Gordon equation and find the QNM spectrum semianalytically and numerically. Interestingly enough, we show that such perturbations are governed by only one parameter μ. Therefore, in D = 4, we find an isospectrality between the wormhole and the BBMB/Extremal Reissner-Nordström black hole. In the spirit of the seminal work of Morris and Thorne, we derive the conditions for traversability and compute the proper time for a traveler to traverse the wormhole. Finally, we discuss possible extensions and future directions for our work.
ER -