物质纯重力场部分的能量-动量张量研究  

A study about the energy-momentum tensor of pure gravitational field part of matter

作　　者：娄太平[1] 

机构地区：[1]东北大学材料与冶金学院,沈阳110004

出　　处：《物理学报》2004年第6期1657-1661,共5页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :5 0 2 740 3 0 );教育部留学回国人员科研启动基金资助的课题~~

摘　　要：认为物质的质量 (能量 )存在形式可分为两部分 ,一部分是以纯物质形式存在的 ,另一部分是以纯重力场形式存在的 .物质质量 (能量 )这两种形式各自对应着相应的能量 动量张量 ,物质总的能量 动量张量可表示为Tμν =T(Ⅰ )μν +T(Ⅱ )μν ,这里 ,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 .通过类比电磁理论 ,定义 :ωμ ≡ -c2 gμ0 g0 0 ,并引入一个反对称张量Dμν =ωμ xν-ων xμ ,则物质纯重力场部分的能量 动量张量为T(Ⅱ )μν =(DμρDρν -gμνDαβDαβ 4 ) 4πG .则包含重力场贡献的重力场方程为Rμν -gμνR 2 =8πG(T(Ⅰ )μν +T(Ⅱ )μν ) c4 .将包含重力场贡献的重力方程应用到一个与时间无关质量为M孤立球对称物质体系 ,可得到其纯物质球体之外的线素为ds2 =- (1 -m r) - 2 dr2 -r2 dθ2 -r2 sin2 θdφ2 +(1 -m r) 2 c2 dt2 ,这里m =GM c2 .In this paper,the existing forms of matter is supposed to be divided into two parts, one is the pure matter part,and another is the pure gravitational field part.The two parts of existing forms of matter are corresponding to their energy_momentum tensors,respectively.So the total energy_momentum tensor of matter can be expressed as T μν =T (Ⅰ) μν +T (Ⅱ) μν ,where T (Ⅰ) μν and T (Ⅱ) μν are energy_momentum tensors of pure matter part and pure gravitational field part,respectively.By analogy with the electromagnetic theory,a vector is defined as: ω μ≡-c 2g μ0 /g 00 , and an antisymmetric tensor is defined as:D μν =  ω μ/  x ν-  ω ν/  x μ,so the energy_momentum tensor of the pure gravitational field part of the matter is supposed to be T (Ⅱ) μν =(D μρ D ρ ν-g μν D αβ D αβ /4)/4 π G. The gravitational field equation which contains pure gravitational field part of matter can be expressed by R μν -g μν R/2=8 π G(T (Ⅰ) μν +T (Ⅱ) μν )/c 4.The theory of the gravitational field which contains the energy_momentum tensor of pure gravitational field part of matter can be used in an isolated globular symmetry for pure matter with mass M ,which is time_independent,and the line_element of time_space for the out side of globular symmetry of pure matter can be obtained by d s 2= -(1-m/r) -2 d r 2-r 2 d θ 2-r 2 sin 2θ d φ 2+(1-m/r) 2c 2 d t 2, where m=GM/c 2.

关 键 词：能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势 

分 类 号：O441[理学—电磁学]