The study of static and stable gravitational fields by using the gravitational field theory including the energy-momentum tensor of the pure gravitational field part of matter

Abstract

In this paper, a general gravitational field theory containing the effect of cosmic constant and the energy_momentum tensor of the pure gravitational field part of matter is proposed. The equation of the grovitational field is Rμν -gμνR/2+λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν )/c4， where λ is Einstein’s cosmic constant， Ｔ（Ⅰ） μν and Ｔ（Ⅱ）μν are energy_ momentum tensor of the p ure matter part and pure gravitational field part, respectively. Ｔ（Ⅱ） μν can be expressed by T(Ⅱ)μν=(DμρＤρ ν-gμνＤαβＤαβ/4)/4πG， where Ｄμν＝ωμ／xν-ων／xμ， and the vector is defined as: ωμ≡-c2gμ0/g00. The several static and stable gravit ational fields, such as the external static metric tensor of an isolated globula r symmetric pure matter which contain Einstein's cosmic constant or that with charge, the external stable metric tensor of a rotation isolated globular symm etric pure matter or that with charge, and the internal static gravitational equ ilibrium in a globular symmetric pure ideal fluid star matter are studied and di scussed respectively by the general gravitational field theory which contains the energy-momentum tensor of pure gravitational field part of matter.