爱因斯坦场方程研究(英文)  

A Study of Einstein Field Equation

在线阅读下载全文

作  者:王学仁[1] WANG Xue-ren(School of Applied Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区:[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出  处:《哈尔滨理工大学学报》2019年第1期145-148,共4页Journal of Harbin University of Science and Technology

摘  要:我们将介绍我们的工作:①把9个关联系数分成两组:涉及■(线加速度)的A组包括Γ■,Γ■,Γ■,Γ■,和Γ■;不涉及■的B组包括Γ■,Γ■,Γ■,和Γ■。②回顾关系式■,这里(■)_r是相对论力学中的线加速度,(■)~N是牛顿力学中的线加速度,γ是洛伦兹因数。③我们已经确定(Γ■)~N=-b~′b^(-1),(Γ■)~N=-c^2b~′b^(-5),(Γ■)~N=b~′b^(-1),(Γ■)~N=-rb^(-2),(Γ■)~N=-rb^(-2)sin^2θ。④我们已经确定(Γ■)_r=(-b~′b^(-1))γ~3,(Γ■)_r=(-c^2b~′b^(-5))γ~3,(Γ■)_r=(b~′b^(-1))γ~3,(Γ■)_r=(-rb^(-2))γ~3,(Γ■)_r=(-rb^(-2)sin^2θ)γ~3。⑤我们已经证明Γ■=A~′/(2A)=-b~′b^(-1),Γ■=A~′/(2B)=-c^2b~′b^(-5),Γ■=b~′/(2B)=b~′b^(-1),Γ■=-rb^(-1)=-rb^(-2),Γ■=-rb^(-1)sin^2θ=-rb^(-2)sin^2θ。(6)我们已经确定(Γ■)■=r^(-1),(Γ■)■=sinθcosθ,(Γ■)■=r^(-1),(Γ■)■=cotθ。⑥我们分析了Schwarzschild解并得出两个结论:■,这表明它和牛顿守恒定律有关。(b)对于弱引力场GM/(c^2r)≪1,B=(1-2GM/(c^2r))^(-1)≈1+2GM/(c^2r)≈1+2GM/(c^2r)+(GM/(c^2r))~2=(1+GM/(c^2r))~2=γ~2,因此,γ=1+GM/(c^2r)=b,这个关系式对强引力场也适用。把这些需要的表达方式带入方程式,并应用关系式,我们能简化方程式。我们已经得到了相对论解:-c^2dτ~2=c^2(1+GM/(c^2r))^(-2)dt^2-(1+GM/(c^2r))~2dr^2-r^2dθ~2-r^2sin^2θdφ~2.In this paper we present our research work:①We divide 9 connection coefficients into two groups:Group A involving(the linear acceleration)includesΓ01^0,Γ00^1,Γ11^1,Γ22^1,和Γ33^1;Group B not involving includesΓ12^2,Γ33^2,Γ13^2,和Γ23^3.②Recalling the relation formula:(r)R=(r)^Nγ^3,where(r)R is the linear acceleration in relativistic mechanics,(r)^N the linear acceleration in Newtoneon mechanics,andγLorrentz factor.③We have determined that(Γ01^0)N=-b′b^-1,(Γ00^1)^N=-c^2b′b^-5,(Γ11^1)^N=b′b^-1,(Γ22^1)^N=-rb^-2,(Γ33^1)N=-rb^-2 sin^2θ.④We have determined that(Γ01^0)r=(-b′b^-1)γ^3,(Γ00^1)r=(-c^2b′b^-5)γ^3,(Γ11^1)r=(b′b^-1)γ^3,(Γ22^1)r=(-rb^-2)γ^3,(Γ33^1)r=(-rb^-2 sin^2θ)γ^3.⑤We have proved thatΓ01^0=A′/(2A)=-b′b^-1,Γ00^1=A′/(2B)=-c^2b′b^-5,Γ11^1=b′/(2B)=b′b^-1,Γ22^1=-rb^-1=-rb^-2,Γ33^1=-rb^-1 sin^2θ=-rb^-2 sin^2θ.(6)We have determined that(Γ12^1)R^N=r^-1,(Γ33^2)R^N=sinθcosθ,(Γ13^3)R^N=r^-1,(Γ23^3)R^N=cotθ.⑥We have analyzed Schwarzschild solution,and drawn two conclusions:(a)B=(1-2GM/(c^2r))-1=(1-r^2/c^2)^-1=γ^2,indicating that it involves Newtoneon formula of energy conservation.(b)In the case of the weak gravitational field,GM/(c^2r)﹤﹤1,B=(1-2GM/(c^2r))^-1≈1+2GM/(c^2r)≈1+2GM/(c^2r)+(GM/(c^2r))^2=(1+GM/(c^2r))^2=γ^2,therefore,γ=1+GM/(c^2r)=b,it holds too,in the case of the strong gravitational field.(8)Substituting the needed expressions into equations,and applying the relation formulas,we can simplify the equations,Obtaining the relativistic solution:-c^2 dτ^2=c^2(1+GM/(c^2r))^-2 d t^2-(1+GM/(c^2r))^2 d r^2-r^2 dθ^2-r^2 sin^2θdφ^2.

关 键 词:广义相对论 场方程 引力理论 

分 类 号:O412.1[理学—理论物理]

 

参考文献:

正在载入数据...

 

二级参考文献:

正在载入数据...

 

耦合文献:

正在载入数据...

 

引证文献:

正在载入数据...

 

二级引证文献:

正在载入数据...

 

同被引文献:

正在载入数据...

 

相关期刊文献:

正在载入数据...

相关的主题
相关的作者对象
相关的机构对象