Would gravitational pull of a wormhole be the average of the two locations that the wormhole connects? I've seen questions here ask if gravitational pull can pass through a wormhole but I havent seen answers that address if lack of gravitational pull would pass through as well.
What I mean is, people ask if they would feel the pull of a blackhole through a wormhole, typically the hypothetical answer is yes. I would like to take it one step further and ask, if one end of the wormhole is in flat space and the other in the vacinity of a massive object, would the field of the wormhole average the two out?
 A: The traversable wormhole requires some form of quantum field with $T^{00}~<~0$. This field as a source of spacetime results in the divergence of geodesics.  Quantum fields or matter that obey the Hawking-Penrose energy conditions, in particular the averaged weak energy condition $T^{00}~\ge~0$, as a source of spacetime geometry result in the focusing of geodesics in spacetime.
A black hole that emits a particle as Hawking radiation loses some of its mass. We may think of the emitted particle as a source of Einstein lensing, which means the horizon region that focuses light is reduced. The emission of a positive mass particle in Hawking radiation may be considered to be associated with the absorption of a negative mass particle by the black hole. As a result there is a role of negative mass with black holes, though the negative mass particle that falls into a black hole may also be thought of as a positive mass particle on a time reversed path that is scattered into the Hawking emitted particle on a positive time path. 
Now suppose we can arrange for a shell of negative mass-energy field that approaches the black hole. From the perspective of a distant observer this shell would be time dilated as it approaches the horizon. This shell would in the tortoise coordinates of the distant observer reduce the size of the horizon, and would in some way contribute to the Hawking evaporation of the black hole in the distant future. This then forms a thin shell just above the horizon. There is then a Lanczos junction condition across this shell. The negative energy condition results in a jump in the curvature across this shell. This paper illustrates the role of the junctions with wormholes. As a result an observer crossing this junction would measure a jump in the spactime physics. 
The gravity field on either side of the junction is tricky to understand. The divergence of geodesics across the junction above horizon if strong enough will result in a multiply connected spacetime. One must adjust this in a sensitive way so the black hole geometry or any other gravity field external to the black hole does not result in an instability. The negative energy condition also means the quantum field has no minimal energy level, or that the spectrum is not bounded below. As a result the wormhole is not entirely stable. The introduction of a gravity field exterior to the wormhole, or if a particle or even the vacuum enters a wormhole it might perturb it so this instability demolishes the wormhole.
