Observing a wormhole

If a traversable wormhole smoothly connects two different spacetimes, then the flux cannot be separately conserved in any of these spaces individually. Then objects propagating in a vicinity of a wormhole in one space must feel influence of objects propagating in the other space. We show this in the cases of the scalar, electromagnetic, and gravitational field. The case of gravity is perhaps the most interesting. Namely, by studying the orbits of stars around the black hole at the center of our galaxy, we could soon tell if this black hole harbors a traversable wormhole. In particular, with a near future acceleration precision of $10^{-6} m/s^2$, a few solar masses star orbiting around Sgr A* on the other side of the wormhole at the distance of a few gravitational radii would leave detectable imprint on the orbit of the S2 star on our side. Alternatively, one can expect the same effect in black hole binary systems, or a black hole - star binary systems. Another result that we find very interesting is that gravitational perturbations can be felt even on the other side of the non-traversable wormhole.