A covariant gravitational field equation including the contribution of gravitational field

Using the four-leg metric tensor lambda mu((a)), a gravitational field 4-vector potential for index mu is defined as omega mu((a)) equivalent to c lambda mu((a)) and a covariant gravitational field equation that includes the gravitational field contribution is proposed as R-mu v - g(mu v) R/2 + Lambda g(mu v) = 8 pi G(T-mu v((I)) + T-mu v((II)))/c(4) where Lambda is Einstein's cosmic constant, T-mu v((I)) and T-mu v((II)) are energy-momentum tensor of pure matter part and pure gravitational field part, respectively. The covariant energy-momentum tensor of gravitational field that belongs to part of the gravitational source can be constructed as T-mu v((II)) =c(2)((D mu pDv(a)p)-D-(a) - g(mu v)D(tau y)((a))D((a))(tau y)/4)4 pi G, where D-mu v((a)) equivalent to omega((a))(mu;v) - omega((a))(v;mu). The static spherically symmetric gravitational field, the missing mass and the gravitational field quantization are discussed.