[danharaj]

Ricci scalar: number assigned to each point of a space describing curvature at that point

Stress-energy tensor (field): multidimensional quantity assigned to each point of a space describing how matter and energy are concentrated and moving at that point.

Trace: coordinate invariant transformation that turns a tensor field into a scalar field.

Diffeomorphism invariant: the object in question has the same description regardless of arbitrary coordinate changes