Wormholes are fascinating alternatives to black hole geometries. In this paper, we have studied a special case of wormhole solution in the context of $R=0$ spacetime. Our approximate analytical calculations show that, under a strictly static axial gravitational perturbation of this spacetime, the magnetic-type tidal Love number (for $\ell =2$) vanishes if we keep the solution of the master equation up to linear order in the regularization parameter of the geometry. Moreover, imposing physically viable boundary conditions on the master variable, we have corroborated our result with the numerical solutions. We have further extended our analysis toward the case of a Damour-Solodukhin wormhole, which also yields a similar conclusion.

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• Alternative gravity theories
• General relativity
• Gravitational waves