Einstein's Energy-Free Gravitational Field

Abstract

We show that Einstein's gravitational field has zero energy, momentum, and stress. This conclusion follows directly from the gravitational field equations, in conjunction with the differential law of energy-momentum conservation $ T^{μν}_{;ν} = 0 $. Einstein rejected this conservation law despite the fact that it is generally covariant. We trace his rejection to a misapplication of Gauss' divergence formula. Finally, we derive the formula which pertains to energy-momentum conservation.