Dynamical Stability and Quasinormal Modes of Casimir Wormholes in dRGT Massive Gravity
Abstract
This paper investigates static, spherically symmetric traversable wormholes supported by Casimir energy within de Rham-Gabadadze-Tolley (dRGT) massive gravity. By deriving the exact shape function b(r) = r0 + (π3(−r + r0))/(90 r r0) − 1/2 C mg2 (r − r0)[2C c2 + c1(r + r0)], we verify that the geometry satisfies the local Morris--Thorne throat and traversability conditions, including b(r0)=r0 and b'(r0)<1. For the nonzero massive-gravity parameters considered here, the resulting spacetime is not asymptotically flat, and its large-r behavior is governed by the massive-gravity contributions to the shape function. The Casimir energy density ρ= −π2/(720 r4) ensures the Null Energy Condition is violated throughout the throat region, as demonstrated by the negative behavior of (ρ+ pr) and (ρ− |pr|) across all parameter values. Analysis of the volume integral quantifier reveals that the massive gravity parameter mg2 c2 directly regulates the exotic matter requirement, with the integrated NEC violation becoming more negative as mg2 c2 increases from $0.1$ to $0.5$. The mechanical equilibrium is rigorously established via the generalized Tolman-Oppenheimer-Volkoff equation, where the anisotropic force precisely balances the gravitational and hydrostatic forces. The quasinormal mode spectrum for scalar perturbations is extracted using both the analytical Mashhoon method and direct numerical integration. The effective potential forms a symmetric barrier at the throat, with the peak height increasing with the multipole number ℓ. The damping rate |ωI| grows systematically with increasing massive gravity parameter. These distinct spectral signatures provide robust theoretical markers for distinguishing Casimir wormholes from black holes in future gravitational wave observations.
Related
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- Traversable Casimir Wormholes with Gravitational Memory
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- Traversable Wormholes Supported by Conformally Coupled Scalar Fields in D ≥ 4: Geometry, Geodesics, and Quasinormal Modes
BibTeX
@misc{bhar2026dynamical,
title = {{Dynamical Stability and Quasinormal Modes of Casimir Wormholes in dRGT Massive Gravity}},
author = {Piyali Bhar and Dhruba Jyoti Gogoi and A. Errehymy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06893},
eprint = {2610.06893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06893},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamical Stability and Quasinormal Modes of Casimir Wormholes in dRGT Massive Gravity
AU - Piyali Bhar
AU - Dhruba Jyoti Gogoi
AU - A. Errehymy
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.06893
UR - https://arxiv.org/abs/2610.06893
AB - This paper investigates static, spherically symmetric traversable wormholes supported by Casimir energy within de Rham-Gabadadze-Tolley (dRGT) massive gravity. By deriving the exact shape function b(r) = r_0 + (π^3(−r + r_0))/(90 r r_0) − 1/2 C m_g^2 (r − r_0)[2C c_2 + c_1(r + r_0)], we verify that the geometry satisfies the local Morris--Thorne throat and traversability conditions, including b(r_0)=r_0 and b'(r_0)<1. For the nonzero massive-gravity parameters considered here, the resulting spacetime is not asymptotically flat, and its large-r behavior is governed by the massive-gravity contributions to the shape function. The Casimir energy density ρ= −π^2/(720 r^4) ensures the Null Energy Condition is violated throughout the throat region, as demonstrated by the negative behavior of (ρ+ p_r) and (ρ− |p_r|) across all parameter values. Analysis of the volume integral quantifier reveals that the massive gravity parameter m_g^2 c_2 directly regulates the exotic matter requirement, with the integrated NEC violation becoming more negative as m_g^2 c_2 increases from $0.1$ to $0.5$. The mechanical equilibrium is rigorously established via the generalized Tolman-Oppenheimer-Volkoff equation, where the anisotropic force precisely balances the gravitational and hydrostatic forces. The quasinormal mode spectrum for scalar perturbations is extracted using both the analytical Mashhoon method and direct numerical integration. The effective potential forms a symmetric barrier at the throat, with the peak height increasing with the multipole number ℓ. The damping rate |ω_I| grows systematically with increasing massive gravity parameter. These distinct spectral signatures provide robust theoretical markers for distinguishing Casimir wormholes from black holes in future gravitational wave observations.
ER -