# Can dark matter and energy be formulated as local perturbations of the metric

Note, my formal physics education ended over ten years ago so I may be missing some obvious piece of understanding.

The relationship between space-time and matter/energy distribution is described by Einstein's field equations:

$$G_{\mu\nu}=8\pi T_{\mu\nu}$$

G is a tensor that describes the geometry of space time, and T describes the distribution of matter, how it's moving, etc. When I read about Dark Matter I presume these are inserted as terms in the stress energy tensor on the right and are then interpreted as mysterious missing matter. Similarly, Dark Energy terms may be added as extra terms on the left, such as the cosmological constant, or further terms in T.

My question is, then, why these cannot be captured as local perturbations to the global curvature. Ie, scale-dependent terms in the Ricci tensor? This would allow for localized gravitational lensing effects and apparent extra mass around massive objects such as galaxies and would just be a property of space-time.

-
The content of the Einstein equation is that any Ricci curvature can be understood as stress energy in space time (after subtracting a multiple of the trace), and so any description of dark matter which jut formally rearranges the curvature side of the equation is equivalent to adding new matter with only gravitational interactions. – Ron Maimon Apr 5 '12 at 3:25