What is the nature of the gravitational field around a object in space? What is physically interacting with the object to inform it about the local field?
The nature of the gravitational field around an object in space is that it is a curvature of spacetime caused by the presence of mass or energy. According to Einstein's theory of general relativity, massive objects cause a distortion of the fabric of spacetime, creating a well that attracts other objects toward it.

As for what is physically interacting with the object to inform it about the local field, it's the same thing that's causing the field in the first place: the presence of mass or energy. The object is experiencing the effects of the field as a result of its interaction with other massive objects in the vicinity.

It's important to note that gravity is a force that acts between masses, and it doesn't require any physical contact or transfer of material between the objects. The interaction is solely due to the curvature of spacetime caused by the masses.