Stability and instability of Ellis and phantom wormholes: Are there ghosts?

It is concluded in the literature that the Ellis wormhole is unstable under small perturbations and would either decay to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to the Schwarzschild black hole only when the Ellis solution parameter $\ensuremath{\gamma}$ assumes a complex value $\ensuremath{-}i$. We shall then reexamine the stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequantal statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamilton's optical-mechanical analogy in a gravity field. A crucial component of Tangherlini's idea is the observed increase of momentum of the photons entering a real medium. We show that this fact has a heuristic parallel in the effective medium version of the Pound-Rebka experiment in gravity. Our conclusion is that there is a nonzero probability that Ellis and phantom wormholes could appear stable or unstable depending on the location of observers and on the values of $\ensuremath{\gamma}$, leading to the possibility of ghost wormholes (like ghost stars). The Schwarzschild horizon, however, would always certainly appear to be stable ($R=1$, $T=0$) to observers regardless of their location. Phantom wormholes of bounded mass in the extreme limit $a\ensuremath{\rightarrow}\ensuremath{-}1$ are also shown to be stable just as the Schwarzschild black hole is. We shall propose a thought experiment showing that our nondeterministic results could be numerically translated into observable deterministic signatures of ghost wormholes.