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 $b(r)=r_0+\frac{{\pi }^3(-r+r_0)}{90r{r}_0}-\frac{1}{2}C{m}_g^2(r-r_0)[2C{c}_2+c_1(r+r_0)]$, we verify that the geometry satisfies the local Morris--Thorne throat and traversability conditions, including $b(r_0)=r_0$ and $b^{\prime }(r_0)<1$. 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 $\rho =-{\pi }^2/(720r^4)$ ensures the Null Energy Condition is violated throughout the throat region, as demonstrated by the negative behavior of $(\rho +p_r)$ and $(\rho -|p_r|)$ 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 $\ell$. The damping rate $|{\omega }_I|$ 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.

arXiv comment28 pages, 18 figures