Generalization of the Einstein Theory

The assumption that ${{T}^{\ensuremath{\nu}}}_{\ensuremath{\mu};\ensuremath{\nu}}=0$ in curved space-time is questioned. Field equations are given which are consistent with the assumption ${{T}^{\ensuremath{\nu}}}_{\ensuremath{\mu};\ensuremath{\nu}}=\ensuremath{\lambda}{R}_{,\ensuremath{\mu}}$, and which reduce to the Einstein equations when $\ensuremath{\lambda}=0$. 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.

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