Would you feel the gravity of a black hole through a wormhole? So, hypothetically, if we were to "accidently" open a Einstein-Rosen bridge and the other side of the wormhole opened with in the gravity well of a blackhole. Would the gravity, and effects of Gravity (time dilation, gravitational pull etc) be experienced by the observers at the point of origin?
 A: First, Einstein-Rosen bridges probably will not let through any effects since they are unstable: they close faster than anything can pass through them, including a lightspeed signal.
However, if we use some other wormhole models then it is likely that gravitational effects can pass though.
The simplest form is when we identify two surfaces with each other, like having a disk or a polyhedron for each opening and topologically glue them together. Here the curvature is zero everywhere except for the edges, where they are infinite. This may not be an entirely realistic wormhole, but it is possible to analyse rigorously what Newtonian gravity and electromagnetism does in such spacetimes (and for weak enough fields this is likely a good approximation). The conclusion for a two-side wormhole (the linked page solves it for a more general spacetime) is that gravity does indeed emerge from the wormhole if there is something heavy on the other side.
The problem with more realistic wormholes (or at least solutions to the GR equations using exotic matter) is that there is no simple way of adding two GR solutions together. One can make arguments that if matter or charge passes through a wormhole continuity will demand that field lines will thread it, leaving a kind of residual gravity or charge. The main problem is that if these become significant compared to the exotic matter densities it is plausible that the wormhole collapses. But proving this rigorously is hard.
