引力场方程的新标架形式及定域化的引力场能量动量张量  

The New Vierbein Form of Gravitational Equations and Localized Energy-Momentum Tensors of Gravitational Field

作　　者：唐飞琳 

机构地区：[1]广州世纪星科技有限公司,广州560000

出　　处：《前沿科学》2010年第4期47-65,共19页Frontier Science

摘　　要：本文通过引入标架空间定义了引力场场强张量和引力场拉格朗日密度,根据最小作用量原理导出了引力场运动方程的一种新的半度规形式(或称标架形式)及具有标架空间和坐标空间的双重协变的引力场能量动量张量。我们用这种定域化的能量表达式和球对称真空外部场席瓦兹希德解(当β1+β2=0,β3=0时)计算出在r≥R区域中的球对称引力场的总能量为E=MC2(1-(1-2GM/C2R)1/2)/(1+(1-2GM/C2R)1/2)它把爱因斯坦引力理论作为一个特例(满足条件β1=β2=β3=0)包含其中,是对爱因斯坦度规引力理论的重大发展。本文通过求解球对称真空外部场解得到以下结论:满足条件β1+β2=0,β3=0时的球对称真空外部场解就是席瓦兹希德外部解,基于球对称真空外部场解的任何检验Einstein引力场方程的实验验证都无法确定Einstein引力场方程是唯一正确的。最后根据粒子在引力场中的运动方程确定了待定常数的值为β1=2β,β2=β3=0。本文得到的引力理论与平移引力理论具有相同的形式。本文建立的引力理论采用的几何是黎曼几何,没有采用平移引力理论中的Weitzenbock几何,并且对其中的能量问题和待定常数问题作了更深入的讨论。In this paper,We has defined the gravitational field intensity tensors and the gravitational field Lagrange density through the introduction of vierbein space-time.According to the principle of least action,an new vierbein(half -metric) form of gravitational field equation and the localized energy-momentum tensors of gravitational field were set up.Using this localized energy-momentum tensors and Schwarzchild's solution,we could find that the total energy of the spherical symmetric gravitational field in the region of r≥R is E=MC2E=MC2(1-(1-2GM/C2R)1/2)/(1+(1-2GM/C2R)1/2).The Einstein gravitational theory is an exceptional case to be contained in it,and It is the significant development of Einstein metric gravitational theory.In this paper,by solving the spherically symmetric vacuum solution of the external field ,the following conclusion has been obtained: at the conditions β1+β2=0,β3=0,the spherically symmetric vacuum solution of the external field is Schwarzchild's external solution.Based on spherically symmetric vacuum solution of the external field,any experimental verification that test Einstein's gravitational field equations can not be sure that Einstein gravitational field equations are the only correct gravitational equations.Finally,we obtained the value of the undetermined constant: β1=2β,β2=β3=0 by the particle equations of motion.The form of the gravitational equations of motion in this paper is same as the equations in the teleparallel gravitational theory.The geometry in this paper is Riemann geometry,not Weitzenbock geometry used in the teleparallel gravitational theory.In this papere,we studied deeply the gravitational field energy and the undetermined constant.

关 键 词：广义相对论 引力场 引力场能量动量张量 内部标架空间 洛仑兹群空间 爱因斯坦引力场运动方程 半度规 

分 类 号：O412.1[理学—理论物理]