Generic spherically symmetric thin-shell wormholes with equilibrium throat at the innermost photonsphere are unstable

In this research, we prove analytically that a generic spherically symmetric thin-shell wormhole (TSW) with its throat located at the innermost photonsphere of the bulk asymptotically flat black hole and supported by a generic surface barotropic perfect fluid is unstable against a radial linear perturbation. This is the generalization of the instability of the Schwarzschild TSW (STSW) with the throat's radius located at $a_{0}=3M$ that was revealed by Poisson and Visser in their seminal work \cite{Poisson1995} where they studied the mechanical stability of STSW. Our proof provides a link between the instability of the null circular geodesics on the innermost photonsphere of a generic static spherically symmetric asymptotically black hole and the TSW constructed in the same bulk with $a_{0}=r_{c}$ where $% a_{0} $ and $r_{c}$ are the radius of the TSW and the innermost photonsphere, respectively. For asymptotically flat spherically symmetric black holes possessing more than one photonspheres, the number of the photonspheres is odd and at least one photonsphere is stable which implies the corresponding TSW with its throat identical with the stable photonsphere is also stable.