含物质纯重力场部分贡献的静态和稳态重力场研究

给出了包含重力场贡献在内具有宇宙因子项最普遍形式的重力场方程为Rμν-gμνR/2+λgμν=8πG(T(Ⅰ)μν+T(Ⅱ)μν)/c4，这里λ为Einstein宇宙常数，Ｔ（Ⅰ）μν，Ｔ（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.物质纯重力场部分的能量-动量张量表述为T(Ⅱ)μν=(DμρＤρν-gμνＤαβＤαβ/4)/4πG，式中Dμν的定义为Ｄμν＝ωμ／xν-ων／xμ，ωμ≡-c2gμ0/g00.并用重力场贡献在内最普遍形式的重力场方程分别研究了几个大家所熟悉的静态和稳态重力场，像带有Einstein宇宙因子λ项球对称纯物质球外部静态度规、静态荷电球外部度规、匀速转动星体外部度规及理想纯物质星体内部静态平衡等,并进行了讨论. 关键词： 能量动量张量 重力场方程 静态重力场 稳态重力场

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

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.