If a star passes near another star will that star feel gravitational influence immediately or with a delay? If a star passes near another star will that star feel gravitational influence immediately or with a delay? Assuming that the distance is a large number and the stars are very massive?
 A: The gravitational field of an object generally moves as though rigidly attached to the object. It doesn't lag behind, so its influence on other objects is similar to a Newtonian field that always updates instantly. There isn't the light-speed delay that you might expect.
This is actually required by the principle of relativity. If an ordinary solid object is at rest in a vacuum and you push a small part of it to start it moving, that part moves before the rest of it at first, but over time the rest of the object catches up; it doesn't permanently lag behind. It can't, because an object in motion is the same as an object at rest, so there is no behind. Only if a part of the object moves in a complicated way that isn't "expected" by the rest of the object do you get update delays. Gravitational and electromagnetic fields work in a similar way.
A: Gravitational fields propagate in the vacuum with the speed of light according to the equations  $\;\;\left(\frac{\partial^{2}}{\partial x^{2}}-\frac{\partial^{2}}{\partial t^{2}}\right)h_{i}^{k}=0\;\; $ (in one dimension to simplify) exactly like electromagnetic field *.
By analogy we can use the Retarded potential **.
(*) Far from the bodies the field is weak, which implies that the space-time metric is almost Galilean, and one can thus use a reference frame in which the components of the metric tensor are almost equal to the Galilean values $\;\;g_{ij}=g_{ij}^{(0)}+h_{ij}\;\;\;\;,g_{00}^{(0)}=1\;\;,g_{0\alpha}^{(0)}=0\;\;,  g_{\alpha\beta}^{(0)}=-\delta_{\alpha\beta}$
(**) The retarded potential in linearized general relativity .
