A recent work by Dey and Sen derived the approximate light deflection angle α by an Ellis wormhole in terms of proper radial distance ℓ that covers the entire spacetime. On the other hand, Bodenner and Will calculated the expressions for light bending in Schwarzschild geometry using various coordinates and showed that they all reduce to a single formula when re-expressed in the coordinate independent language of "circumferential radius" rC identified with the standard radial coordinate rS. We shall argue that the coordinate invariant language for two-way wormholes should be ℓ rather than rS. Hence here we find the exact deflection α in Ellis wormhole geometry first in terms of ℓ and then in terms of rS. We confirm the latter expression using three different methods. We argue that the practical measurement scheme does not necessarily single out either ℓ or rS. Some errors in the literature are corrected.

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 only when the Ellis solution parameter γ 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 1 arXiv:1606.04356v1 [gr-qc] 6 Jun 2016 statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamilton's opticalmechanical 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 γ, leading to the possibility of 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 → −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.

Recently, it has been shown by Lobo, Parsaei and Riazi (LPR) that phantom energy with $\omega =p_{r}/\rho <-1$ could support phantom wormholes. Several classes of such solutions have been derived by them. While the inner spacetime is represented by asymptotically flat phantom wormhole that have repulsive gravity, it is most likely to be unstable to perturbations. Hence, we consider a situation, where a phantom wormhole is somehow trapped inside a Schwarzschild sphere across a thin shell. Applying the method developed by Garcia, Lobo and Visser (GLV), we shall exemplify that the shell can possess zones of stability depending on certain constraints. It turns out that zones corresponding to "force" constraint are more restrictive than those from the "mass" constraint. We shall also enumerate the interior energy content by using the gravitational energy integral proposed by Lynden-Bell, Katz and Bi% \v{c}\'ak. It turns out that, even though the interior mass is positive, the integral implies repulsive energy. This is consistent with the phantom nature of interior matter.Comment: 10 pages, 3 figures, Indian J Phys 201

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In this paper, we wish to investigate certain observable effects in the recently obtained wormhole solution of the EiBI theory, which generalizes the zero mass Ellis-Bronnikov wormhole of general relativity. The solutions of EiBI theory contain an extra parameter κ having the inverse dimension of the cosmological constant Λ, and is expected to modify various general relativistic observables such as the masses of wormhole mouths, tidal forces and light deflection. A remarkable result is that a non-zero κ could prevent the tidal forces in the geodesic orthonormal frame from becoming arbitrarily large near a small throat radius (r 0 ∼ 0) contrary to what happens near a small Schwarzschild horizon radius (M ∼ 0). The role of κ in the flare-out and energy conditions is also analysed, which reveals that the energy conditions are violated. We show that the exotic matter in the EiBI wormhole cannot be interpreted as phantom (ω = pr ρ < −1) or ghost field φ of general relativity due to the fact that both ρ and p r are negative for all κ.