Curvature is a property of spaces. But the Einstein equation does say that the mathematical quantity called the Einstein tensor field is equivalent to the physical quantity called the energy-momentum density tensor field. Even though energy-momentum is associated with physical objects, the Einstein tensor field is still a property of spacetime.

What about objects like fluids?Can they be modeled using the concept of curvature? Can the motion of an object through a variably dense medium also be modeled like this?

Quote:

Originally Posted by

**geordief**
To reassure myself that I am getting my ducks in a row ,when discussing intrinsic curvature are we here modeling physical /and or mathematical objects as __sets of points__**?

**(that's a manifold,I think)

The notion of intrinsic curvature goes way beyond the notion of "sets of points". It should be noted that the debate between Guitarist and myself was a debate about the appropriate level of generality to apply to the discussion. Mathematical notions are defined in terms of satisfying a given set of axioms. However, if one has the definition of a particular mathematical notion, then one can define specialised forms of that notion by adding more axioms to the original definition. Even a notion as general as topological spaces goes beyond mere sets of points. Manifolds are more special than topological spaces, but even these do not have the axioms necessary to equip the notion with curvature. Manifolds require additional axioms that define a connection in order for them to be equipped with the notion of curvature. However, I've gone a little bit further and considered not just manifolds equipped with a connection but manifolds equipped with a metric, as it is these that correspond to macroscopic physical spacetime.