[1]王学仁. 爱因斯坦场方程研究[J].哈尔滨理工大学学报,2019,(01):145-149.[doi:10.15938/j.jhust.2019.01.024]
 WANG Xue ren. A Study of Einstein Field Equation[J].哈尔滨理工大学学报,2019,(01):145-149.[doi:10.15938/j.jhust.2019.01.024]
点击复制

 爱因斯坦场方程研究

()
分享到:

《哈尔滨理工大学学报》[ISSN:1007-2683/CN:23-1404/N]

卷:
期数:
2019年01期
页码:
145-149
栏目:
管理科学与工程
出版日期:
2019-08-06

文章信息/Info

Title:
 A Study of Einstein Field Equation

作者:
 王学仁
 (哈尔滨理工大学 应用科学学院,黑龙江 哈尔滨 150080)
Author(s):
 WANG Xueren
 (School of Applied Science, Harbin University of Science and Technology, Harbin 150080, China)
关键词:
 关键词:广义相对论场方程引力理论
Keywords:
 Keywords:general relativity field equation gravitational theory
分类号:
O412.1
DOI:
10.15938/j.jhust.2019.01.024
文献标志码:
A
摘要:
 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〖AKr¨D〗(线加速度)的A组包括Γ001,Γ100, Γ111, Γ122, 和 Γ133;不涉及〖AKr¨D〗的B组包括Γ212, Γ233, Γ313, 和 Γ323。②回顾关系式(〖AKr¨D〗)r=(〖AKr¨D〗)Nγ3,这里(〖AKr¨D〗)r是相对论力学中的线加速度,(〖AKr¨D〗)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001)N=-b′b-1,(Γ100)N=-c2b′b-5,(Γ111)N=b′b-1,(Γ122)N=-rb-2,(Γ133)N=-rb-2sin2θ。④我们已经确定(Γ001)r=(-b′b-1)γ3, (Γ100)r=(-c2b′b-5)γ3,(Γ111)r=(b′b-1)γ3,(Γ122)r=(-rb-2)γ3,(Γ133)r=(-rb-2sin2θ)γ3。⑤我们已经证明Γ001=A′/(2A)=-b′b-1, Γ100=A′/(2B)=-c2b′b-5,Γ111=b′/(2B)=b′b-1,Γ122=-rb-1=-rb-2,Γ133=-rb-1sin2θ=-rb-2sin2θ。(6)我们已经确定(Γ112)Nr=r-1,(Γ233)Nr=sinθcosθ,(Γ313)Nr=r-1,(Γ323)Nr=cotθ。⑥我们分析了Schwarzschild解并得出两个结论:(a)B =(1-2GM/(c2r))-1=(1-r〖DD(-2mm〗·〖DD)〗2/c2)-1=γ2,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2dτ2=c2(1+GM/(c2r))-2dt2-(1+GM/(c2r))2dr2-r2dθ2-r2sin2θdφ2.

 

Abstract:
 Abstract:In this paper we present our research work: ①We divide 9 connection coefficients into two groups: Group A involving 〖AKr¨D〗 (the linear acceleration) includes Γ001,Γ100, Γ111, Γ122, and Γ133; Group B not involving 〖AKr¨D〗 includes Γ212, Γ233, Γ313, and Γ323. ②Recalling the relation formula: (〖AKr¨D〗)R=(〖AKr¨D〗)Nγ3, where (〖AKr¨D〗)R is the linear acceleration in relativistic mechanics, (〖AKr¨D〗)N the linear acceleration in Newtoneon mechanics, and γ Lorrentz factor. ③We have determined that (Γ001)N= -b′b-1, (Γ100)N= -c2b′b-5, (Γ111)N= b′b-1, (Γ122)N= -rb-2, (Γ133)N= -rb-2sin2θ. ④We have determined that (Γ001)R = (-b′b-1)γ3, (Γ100)R = (-c2b′b-5)γ3, (Γ111)R = (b′b-1)γ3, (Γ122)R = (-rb-2)γ3, (Γ133)R = (-rb-2sin2θ)γ3. ⑤We have proved that Γ001=A′/(2A)=-b′b-1, Γ100 = A′/(2B) = -c2b′b-5, Γ111 = B′/(2B) = b′b-1, Γ122 = -rB-1 = -rb-2,Γ133 = -rB-1sin2θ= -rb-2sin2θ. (6)We have determined that (Γ112)NR = r-1, (Γ233)NR = sinθcosθ, (Γ313)NR= r-1, (Γ323)NR = cotθ. ⑥We have analyzed Schwarzschild solution, and drawn two conclusions: (a)B=(1-2GM/(c2r))-1 = (1-r〖DD(-2mm〗·〖DD)〗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dτ2 = c2(1+GM/(c2r))-2dt2 - (1+GM/(c2r))2dr2-r2dθ2-r2sin2θdφ2

相似文献/References:

[1]孙永全,郭建英,陈洪科,等.AMSAA模型可靠性增长预测方法的改进[J].哈尔滨理工大学学报,2010,(05):49.
 SUN Yong-quan,GUO Jian-ying,CHEN Hong-ke,et al.An Improved Reliability Growth Prediction Algorithm Based on AMSAA Model[J].哈尔滨理工大学学报,2010,(01):49.
[2]滕志军,李晓霞,郑权龙,等.矿井巷道的MIMO信道几何模型及其信道容量分析[J].哈尔滨理工大学学报,2012,(02):14.
 TENG Zhi-jun,LI Xiao-xia,ZHENG Quan-long.Geometric Model for Mine MIMO Channels and Its Capacity Analysis[J].哈尔滨理工大学学报,2012,(01):14.
[3]李艳苹,张礼勇.新训练序列下的改进OFDM符号定时算法[J].哈尔滨理工大学学报,2012,(02):19.
 LI Yan-ping,ZHANG Li-yong.An Improved Algorithm of OFDM Symbol Timing Based on A New Training Sequence[J].哈尔滨理工大学学报,2012,(01):19.
[4]赵彦玲,车春雨,铉佳平,等.钢球全表面螺旋线展开机构运动特性分析[J].哈尔滨理工大学学报,2013,(01):37.
 ZHAO Yan-ling,CHE Chun-yu,XUAN Jia-ping,et al.[J].哈尔滨理工大学学报,2013,(01):37.
[5]李冬梅,卢旸,刘伟华,等.一类具有连续接种的自治SEIR传染病模型[J].哈尔滨理工大学学报,2013,(01):73.
 LI Dong-mei,LU Yang,LIU Wei-hua.[J].哈尔滨理工大学学报,2013,(01):73.
[6]华秀英,刘文德.奇Hamiltonian李超代数偶部的非负Z-齐次导子空间[J].哈尔滨理工大学学报,2013,(01):76.
 HUA Xiu-ying,LIU Wen-de.[J].哈尔滨理工大学学报,2013,(01):76.
[7]桂存兵,刘洋,何业军,等.基于LCC谐振电路阻抗匹配的光伏发电最大功率点跟踪[J].哈尔滨理工大学学报,2013,(01):90.
 GUI Cun-bing,LIU Yong,HE Ye-jun.[J].哈尔滨理工大学学报,2013,(01):90.
[8]翁凌,闫利文,夏乾善,等.PI/TiC@Al2O3复合薄膜的制备及其电性能研究[J].哈尔滨理工大学学报,2013,(02):25.
 WENG Ling,YAN Li-wen,XIA Qian-shan.[J].哈尔滨理工大学学报,2013,(01):25.
[9]姜彬,林爱琴,王松涛,等.高速铣刀安全性设计理论与方法[J].哈尔滨理工大学学报,2013,(02):63.
 JIANG Bin,LIN Ai-qin,WANG Song-tao,et al.[J].哈尔滨理工大学学报,2013,(01):63.
[10]李星纬,李晓东,张颖彧,等.EVOH 磺酸锂电池隔膜的制备及微观形貌[J].哈尔滨理工大学学报,2013,(05):18.
 LI Xing- wei,LI Xiao- dong,ZHANG Ying- yu,et al.The Preparation and Microcosmic Morphology oEVOH- SO Li Lithium Ion Battery Septum[J].哈尔滨理工大学学报,2013,(01):18.

备注/Memo

备注/Memo:
[1]FOSTER J., Nightingale J.D.A short Course in General Relativity[M]. SecondEdition. 1995. New York: Springer Verlag, Chaps 2, 3.
[2]RINDLER W. Introduction to Special Relativity[M]. Oxford: Clarendon press,1982.
更新日期/Last Update: 2019-03-26