Comment on “Observing a wormhole”

Abstract

In their recent paper Dai and Stojkovic discuss an interesting possibility: a star near a wormhole mouth may gravitationally feel an object located near the other mouth. This means that a star's trajectory may tell an observer that the star orbits a wormhole mouth and not a black hole. I argue that within the approximation used in the paper the effect is, in fact, unobservable irrespective of how accurate the measurements are.There is almost consensus that the massive compact objects in the centers of galaxies are giant black holes. There is, however, an alternative point of view, advocated by Kardashev e. a. [1]. According to it, these objects are mouths of wormholes. It would be important therefore, to find effects distinguishing between these two possibilities, see [2,3], in particular. One such effect has been discovered recently [4] by Dai and Stojkovic (DS). They noticed that a star orbiting a wormhole mouth may be affected by perturbations in the gravitational field that are produced by an object orbiting the other mouth.To estimate the effect DS consider a wormhole obtained by gluing together the tubes r 1,2 = R in a pair of equal portions r 1,2 ≥ R > r g of Schwarzschild space. Here r 2,1 are the radial coordinates in, correspondingly, "our universe" (the half of the spacetime in which the test star orbits) and the "other universe", to which the wormhole leads. Now suppose there is an object of a small mass µ in the "other universe" at r 1 = A > R (so, the object is approximated by a light sphere); the radius, A, can-quasistatically-vary. The metrics in our and in the other universes differ from that in the case µ = 0 by perturbations h our and h oth which are assumed to obey the following conditions: (i) only the components h our tt , h our rr , h oth tt , and h oth rr are non-zero;(2) the perturbations depend only on r 1,2 ; (3) h our αβ (R) = h oth αβ (R) and ∂ r2 h our αβ | r2=R = ∂ r1 h our αβ | r1=R [5]. Applying these conditions to the expression for the monopole perturbations borrowed from [4, Ref. (35)], DS infer thatwhere the "additional acceleration" a(M, τ ) is the difference between the total acceleration a tot (τ ) of a (nonrelativistic) test star, and the acceleration a M (τ ) experienced by the same star [6] in the Schwarzschild space with mass M a(M, τ ) ≡ a tot (τ ) − a M (τ ) (2)

Transmission of low-energy scalar waves through a traversable wormhole

“…The solution of the scattering problem for a short-range potential v(x) means the determination of its reflection and transmission amplitudes. According to (24), this is equivalent to finding the transfer matrix of the potential. The transfer matrix has been used as an effective tool for the study of wave propagation in multilayer media since the 1940's [57][58][59][60].…”

“…[21,22] suggest using the gravitational lensing effects for probing wormholes, while Refs. [23][24][25][26] study the effects of the gravitational pull a e-mail: b.azad@alumni.iut.ac.ir b e-mail: loran@iut.ac.ir c e-mail: amostafazadeh@ku.edu.tr (corresponding author) of the objects residing in the vicinity of one of the mouths of a wormhole on the trajectory of objects hovering around the other mouth. These studies together with the spectroscopic techniques [27] should, in principle, offer useful methods to decide whether a given celestial body is a traversable wormhole [28].…”

Transmission of low-energy scalar waves through a traversable wormhole

“…Finally, we use (23) and (48) to derive the following asymptotic expressions for the reflection and transmission amplitudes.…”

“…[20,21] suggest using the gravitational lensing effects for probing wormholes, while Refs. [22,23] study the effects of the gravitational pull of the objects residing in the vicinity of one of the mouths of a wormhole on the trajectory of objects hovering around the other mouth. These studies together with the spectroscopic techniques [24] should, in principle, offer useful methods to decide whether a given celestial body is a traversable wormholes [25].…”