general relativity - Is every solution of Einstein field equations unique?

Einstein's equation is

$$8 \pi T_{ab} = G_{ab},$$

where the left side contains the stress-energy tensor and the right side contains the Einstein tensor.

Is there exactly one unique stress-energy tensor corresponding to a given spacetime curvature? Or is it possible for one curvature (i.e. one spacetime metric) to be produced by multiple different mass configurations?