Can wormholes have vanishing Love numbers?

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 regularisation 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 towards the case of Damour-Solodukhin wormhole, which also yields similar conclusion.