(I'm still working on the Einstein field equation section. Probably keep that portion seperate to minimize length)
This question is amongst one of the most commonly asked questions in relativity. Numerous articles both in pop media and peer reviewed articles refer to terms such as space time fabric, space time curvature. This leads the new learners with a common misconception that space has some mysterious fabric or material like property.
To answer this properly we need to describe a few principles.
A) gravity influences mass
B) energy is a property of particles, or physical configurations such as feilds. Energy does not exist on its own.
C) space is defined as a volume only. That volume contains the standard model particles and feilds. It is not something form of ether. In GR space is mapped in an arbitrary coordinate system. Without the time component the coordinates are in 3d.
D) spacetime is any metric that includes the time component as a vector. This is the 4th dimension, in GR the time component is treated in coordinate form.
E) General relativity is a coordinate system metric. This coordinate system makes use of manifolds. Which is a topological space that is resembles Euclidean space at beach point. For example a Euclidean space (flat space), can undergo a homeomorphism to curved space via relativistic effects such as inertia and mass to an observer.
The rubber sheet example is one such homeomorphism.
A good YouTube video is
Keep in mind the rubber sheet analogy is just that. An analogy, it was never intended to state that space time is a materialistic fabric or ether.
A classical example of a homeomorphism is the coordinate change from Cartesian coordinates (Euclidean flat space) to polar coordinates. (Curved, spherical geometry)
Now with those in mind, we find that spacetime curvature is a geometric coordinate relation of how the strength of gravity influences the particles that reside in the volume of space. In short it is a geometric description of how gravity influences particles not the volume of space.
The terms fabric, curvature, sretches are misleading. They are analogies used to explain the change in geometric relations.
2) How is space time created?
The volume of space simply increases, space itself is just volume filled with the standard model particles.
Edited by Mordred, 1 June 2015 - 01:59 AM.