Abstract
Using the four-leg metric tensor λ(α)μ, a gravitational field 4-vector potential for index μ is defined as ω(α)μ≡-cλ(α)μ, and a covariant gravitational field equation that includes the gravitational field contribution is proposed as Rμν-gμνR/2+Λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν)/c4, where Λ is Einstein's cosmic constant， T(Ⅰ)μν and T(Ⅱ)μν 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 the part of the gravitational source can be constructed as T(Ⅱ)μν=c2(D(α)μρDρν(α)-gμνD(α)τγDτγ(α)/4)/4πG, where D(α)μν≡ω(α)μ;ν-ω(α)ν;μ. The static spherically symmetric gravitational field, the missing mass and the gravitational field quantization are discussed.
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