I found the following definitions:
The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime.
Flux is a simple and ubiquitous concept throughout physics and applied mathematics describing the flow of a physical property in space, frequently also with time variation. It is the basis of the field concept in physics and mathematics.
So I presume from above that the property which flows in GR is energy and/or momentum. Is this a correct?
Under what circumstances does it flow? and from where to where?