Exact scalarization thresholds and onset laws for a nonminimally coupled scalar field on the Ellis wormhole
Abstract
We study a real scalar field nonminimally coupled to curvature on a fixed Ellis wormhole background. The scalar perturbation decouples at linear order, and the substitution $ x=a \tan z $ reduces its static radial equation to a trigonometric Pöschl-Teller problem. This yields the exact threshold spectrum $ ζ_{n\ell}=(n+\ell+1)^2/2 $, closed-form Gegenbauer profiles, and an exact count of negative radial eigenvalues in each angular sector. The s-wave thresholds are zero-energy resonances at which the growth rate rises linearly, whereas the $ \ell \geq1\ $ threshold states are square integrable and the growth rate rises as a square root. At the first threshold we also obtain the next-order term, $ σa=(π/4)g-(3π/16)g^2+O(g^3) $ with $g=2ζ-1 $. For a probe field with quartic self-interaction, we show that no nontrivial spherical static solution exists for $ζ\leq1/2 $ and derive local branch expansions near the s-wave thresholds. Numerical evolutions are consistent with saturation on the nodeless branch. These nonlinear results refer to the probe-field model; they do not establish the existence or stability of fully backreacted scalarized wormholes.
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BibTeX
@misc{guvendi2026exact,
title = {{Exact scalarization thresholds and onset laws for a nonminimally coupled scalar field on the Ellis wormhole}},
author = {Abdullah Guvendi and Omar Mustafa and Claudio Furtado},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00541},
eprint = {2611.00541},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00541},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact scalarization thresholds and onset laws for a nonminimally coupled scalar field on the Ellis wormhole
AU - Abdullah Guvendi
AU - Omar Mustafa
AU - Claudio Furtado
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00541
UR - https://arxiv.org/abs/2611.00541
AB - We study a real scalar field nonminimally coupled to curvature on a fixed Ellis wormhole background. The scalar perturbation decouples at linear order, and the substitution $ x=a \tan z $ reduces its static radial equation to a trigonometric Pöschl-Teller problem. This yields the exact threshold spectrum $ ζ_{n\ell}=(n+\ell+1)^2/2 $, closed-form Gegenbauer profiles, and an exact count of negative radial eigenvalues in each angular sector. The s-wave thresholds are zero-energy resonances at which the growth rate rises linearly, whereas the $ \ell \geq1\ $ threshold states are square integrable and the growth rate rises as a square root. At the first threshold we also obtain the next-order term, $ σa=(π/4)g-(3π/16)g^2+O(g^3) $ with $g=2ζ-1 $. For a probe field with quartic self-interaction, we show that no nontrivial spherical static solution exists for $ζ\leq1/2 $ and derive local branch expansions near the s-wave thresholds. Numerical evolutions are consistent with saturation on the nodeless branch. These nonlinear results refer to the probe-field model; they do not establish the existence or stability of fully backreacted scalarized wormholes.
ER -