Does mass just cause a volume of spacetime to curve or is it -its gravitational field- also a local extension of spacetime itself?

Question

As seen from outside the gravitational field of an object (a black hole, say) in (where the field is very weak) clocks inside the field are observed to run at a slower pace, the length of measuring rods to look shorter nearer to its source as the field is stronger compared to the field at the observer. Does this mean that the rest energy of the object just warps an already existing spacetime (which exists even in the absence of the object) or is the field itself to some extent a local extension of spacetime -in which case the creation of energy would be the creation of spacetime?

Answer 1

The Einstein equations answer your question, the curvature of the space time is related to the mass, which is related to the energy. The concept of gravitational field is one from Newtonian mechanics, and is replaced by curvature of spacetime in General Relativity.