  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.
