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

TL;DR

This paper reevaluates the stability of Ellis and phantom wormholes using a novel optical-mechanical analogy approach, revealing that their stability may depend on observer location and parameters, leading to the concept of 'ghost wormholes' with potential observable signatures.

Contribution

It introduces a non-deterministic, optical-mechanical framework to analyze wormhole stability, challenging prior deterministic conclusions and proposing the existence of ghost wormholes.

Findings

Ellis wormholes are not necessarily unstable; stability depends on observer location and parameters.

A non-zero probability exists for wormholes to appear stable or unstable, implying ghost wormholes.

Phantom wormholes with bounded mass in the extreme limit are stable like Schwarzschild black holes.

Abstract

It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either 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 Schwarzschild black hole \textit{only} when the Ellis solution parameter $\gamma $ assumes a complex value $-i$. We shall then reexamine 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 non-zero probability that Ellis and phantom wormholes could appear stable or unstable depending on the location of observers and on the values of $\gamma$, leading to the possibility of \textit{ghost wormholes} (like ghost stars). The Schwarzschild horizon, however, would always appear certainly stable ($R=1$, $T=0$) to observers regardless of their location. Phantom wormholes of bounded mass in the extreme limit $a\rightarrow -1$ are also shown to be stable just as the Schwarzschild black hole is. We shall propose a thought experiment showing that our non-deterministic results could be numerically translated into observable deterministic signatures of ghost wormholes.