Generalization of the Einstein Theory

The assumption that T^ν_μ;ν=0 in curved space-time is questioned. Field equations are given which are consistent with the assumption T^ν_μ;ν=λR_,μ, and which reduce to the Einstein equations when λ=0. The equations are equivalent to the Einstein equations in empty space-time, but differ from them in the presence of matter. Applications to cosmology, stellar structure, and collapsing objects are suggested.