Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Free particle geodesic affine parameter time-space coordinate systems

Bian Bao-Min Lai Xiao-Ming Yang Lin Li Zhen-Hua He An-Zhi

Citation:

Free particle geodesic affine parameter time-space coordinate systems

Bian Bao-Min, Lai Xiao-Ming, Yang Lin, Li Zhen-Hua, He An-Zhi
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • Taking the time-series t as independent variable, the parameter equations {Xi(t)} of free particle space geodesic can be given. By transforming affine parameter R(t) we achieve homogeneous geodesic differential equations, and derive the first-order differential equations which are satisfied by affine parameter R and the sequence of analytical solutions R marked by rational number Cu. In light of R we define the distance unit of flat four-dimensional coordinate system {t,r,θ,φ}, and then establish a free particle geodesic affine parameter time-space coordinate system {t,ξ,θ,φ}. By the study of the diagonalization process of special relativity time-space interval model metric tensor g in {t,ξ,θ,φ}, we find the spatial and temporal line characteristic quantities t1(t,ξ), τ1(τ,ξ),tt(t,τ,ξ) and ττ1(t,τ,ξ) corresponding to diagonal metric. Derived from these quantities, the dimension of time-space coordinate system is less than 4.
    [1]

    Weinberg S 1980 Gravitation and Cosmology (1st Ed.) (Beijing: Science Press) p168, 468 (in Chinese) [温伯格 S 1980 引力论和宇宙论 (第一版) (北京:科学出版社) 第168, 468页]

    [2]

    Liang C B, Zhou B 2006 Introduction to Differential Geometry and General Relativity (Beijing: Science Press) p69, 190, 192 (in Chinese) [梁灿彬, 周彬 2006 微分几何入门与广义相对论(北京:科学出版社) 第69, 190, 192页]

    [3]

    Pope A C, Matsubara T, Szalay A S, Blanton M R, Eisenstein D J, Gray J, Lain B, Bahcall N A, Brinkmann J, Budavari T, Connolly A J, Frieman J A, Gunn J E, Johnston D, KentS M, Lupton R H, Meiksin A, Nichol R C, Scranton R, Strauss M A, Szapudi I, Tegmark M, Vogeley M S, Weinberg D H, Zehavi I 2004 Astrophys J. 607 655

    [4]

    Bennett C L, Hill R S, Hinshaw G, Nolta M R, Odegard N, Page L, Spergel D N, Weiland J L, Wright E L, Halpem M, Larosik N, Kogut A, Limon M, Meyer S S, Tucker G S, Wollack E 2003 The Astrophysical Journal 148 97

    [5]

    Mather J C, Cheng E S, Cottingham D A, Eplee R E, Fixsen D J, Hewagama T 1994 The Amer. Astro. Soc. 420 439

    [6]

    Benítez N, Riess A, Nugent P, Dickingson M, Chornock E, Filippenko V 2002 The Astrophysical Journal 577 L1

    [7]

    Riess A G, Filippenko A V, Challis P, Clocchiattia A, Diereks A, Gamavich P M, Gilliland R L, Hogan C J, Jha S, Kirshner R P, Lebundgut B, Phillips M M, Reiss D, Schmidt B P, Schommer R A, Smith R C, Spyromilio J, Stubbs C, Suntzeff N B, Tonry J 1998 Astron. J. 116 1009

    [8]

    Schmidt B P, Suntzeff N B, Phillips M M, Schommer R A, Clocchiatti A, Kirshner R P, Garnavich P, Challis P, Leibundgut B, Spyromilio J, Riess A G, Filippenko A V, Hamuy M, Smith R C, Hogan C, Stubbs C, Diercks A, Reiss D, Gilliland R, Tonry J, Maza J, Dressler A, Walsh J, Ciardullo R 1998 The Astrophysical Journal 507 46

    [9]

    Cai R G 2007 Phys. Lett. B 657 228

    [10]

    Zhai X H, Zhao Y B 2006 Chin. Phys. 15 2465

    [11]

    Feng B, Wang X L, ZhangX M 2005 Phys. Lett. B 607 35

    [12]

    Li M 2004 Phys. Lett. B 603 1

    [13]

    Carroll S M 2001 Living Rev. Rel 4 1

    [14]

    Kamenshchik A Y, Moschella U, Pasquier V 2001 Phys. Lett. B 511 265

    [15]

    Nottale L 2010 Found. Sci. 15 101

    [16]

    Sorrell W H 2009 Astrophys. Space. Sci. 323 205

    [17]

    Avinash K, Rvachev V L 2000 Foundations of Physics 30 139

    [18]

    Hawking S W, Ellis G F R 2006 The Large Scale Structure of Space-Time (Changsha: Hunan Science and Technology Press) p30 (in Chinese) [霍金 S W, 埃利斯 G F R 2006 时空的大尺度结构(长沙:湖南科学技术出版社) 第30页]

    [19]

    Lai X M, Bian B M, Yang L, Yang J, Bian N, Li Z H, He A Z 2008 Acta. Phys. Sin. 57 7955 (in Chinese) [赖小明, 卞保民, 杨玲, 杨娟, 卞牛, 李振华, 贺安之 2008 物理学报 57 7955]

    [20]

    Bian B M, Lai X M, Yang L, Li Z H, He A Z 2012 Acta. Phys. Sin. 61 080401 (in Chinese) [卞保民, 赖小明, 杨玲, 李振华, 贺安之 2012 物理学报 61 080401]

    [21]

    Yu Y Q 1997 Introduction of general relativity (Beijing: Peking University Press) p18, 133, 158 (in Chinese) [愈允强 1997 广义相对论引论 (北京:北京大学出版社) 第18, 133, 158页]

    [22]

    Zhu H, Ji C C 2011 Fractal theory and its applications (Beijing: Science Press) p23 (in Chinese)[朱华, 姬翠翠 2011 分形理论及应用(北京:科学出版社) 第23页]

    [23]

    Yu Y Q 2002 Cosmophysics lectures (Beijing: Peking University Press) p104, 105, 214 (in Chinese)[俞允强 2002 物理宇宙学讲义(北京:北京大学出版社) 第104, 105, 214页]

  • [1]

    Weinberg S 1980 Gravitation and Cosmology (1st Ed.) (Beijing: Science Press) p168, 468 (in Chinese) [温伯格 S 1980 引力论和宇宙论 (第一版) (北京:科学出版社) 第168, 468页]

    [2]

    Liang C B, Zhou B 2006 Introduction to Differential Geometry and General Relativity (Beijing: Science Press) p69, 190, 192 (in Chinese) [梁灿彬, 周彬 2006 微分几何入门与广义相对论(北京:科学出版社) 第69, 190, 192页]

    [3]

    Pope A C, Matsubara T, Szalay A S, Blanton M R, Eisenstein D J, Gray J, Lain B, Bahcall N A, Brinkmann J, Budavari T, Connolly A J, Frieman J A, Gunn J E, Johnston D, KentS M, Lupton R H, Meiksin A, Nichol R C, Scranton R, Strauss M A, Szapudi I, Tegmark M, Vogeley M S, Weinberg D H, Zehavi I 2004 Astrophys J. 607 655

    [4]

    Bennett C L, Hill R S, Hinshaw G, Nolta M R, Odegard N, Page L, Spergel D N, Weiland J L, Wright E L, Halpem M, Larosik N, Kogut A, Limon M, Meyer S S, Tucker G S, Wollack E 2003 The Astrophysical Journal 148 97

    [5]

    Mather J C, Cheng E S, Cottingham D A, Eplee R E, Fixsen D J, Hewagama T 1994 The Amer. Astro. Soc. 420 439

    [6]

    Benítez N, Riess A, Nugent P, Dickingson M, Chornock E, Filippenko V 2002 The Astrophysical Journal 577 L1

    [7]

    Riess A G, Filippenko A V, Challis P, Clocchiattia A, Diereks A, Gamavich P M, Gilliland R L, Hogan C J, Jha S, Kirshner R P, Lebundgut B, Phillips M M, Reiss D, Schmidt B P, Schommer R A, Smith R C, Spyromilio J, Stubbs C, Suntzeff N B, Tonry J 1998 Astron. J. 116 1009

    [8]

    Schmidt B P, Suntzeff N B, Phillips M M, Schommer R A, Clocchiatti A, Kirshner R P, Garnavich P, Challis P, Leibundgut B, Spyromilio J, Riess A G, Filippenko A V, Hamuy M, Smith R C, Hogan C, Stubbs C, Diercks A, Reiss D, Gilliland R, Tonry J, Maza J, Dressler A, Walsh J, Ciardullo R 1998 The Astrophysical Journal 507 46

    [9]

    Cai R G 2007 Phys. Lett. B 657 228

    [10]

    Zhai X H, Zhao Y B 2006 Chin. Phys. 15 2465

    [11]

    Feng B, Wang X L, ZhangX M 2005 Phys. Lett. B 607 35

    [12]

    Li M 2004 Phys. Lett. B 603 1

    [13]

    Carroll S M 2001 Living Rev. Rel 4 1

    [14]

    Kamenshchik A Y, Moschella U, Pasquier V 2001 Phys. Lett. B 511 265

    [15]

    Nottale L 2010 Found. Sci. 15 101

    [16]

    Sorrell W H 2009 Astrophys. Space. Sci. 323 205

    [17]

    Avinash K, Rvachev V L 2000 Foundations of Physics 30 139

    [18]

    Hawking S W, Ellis G F R 2006 The Large Scale Structure of Space-Time (Changsha: Hunan Science and Technology Press) p30 (in Chinese) [霍金 S W, 埃利斯 G F R 2006 时空的大尺度结构(长沙:湖南科学技术出版社) 第30页]

    [19]

    Lai X M, Bian B M, Yang L, Yang J, Bian N, Li Z H, He A Z 2008 Acta. Phys. Sin. 57 7955 (in Chinese) [赖小明, 卞保民, 杨玲, 杨娟, 卞牛, 李振华, 贺安之 2008 物理学报 57 7955]

    [20]

    Bian B M, Lai X M, Yang L, Li Z H, He A Z 2012 Acta. Phys. Sin. 61 080401 (in Chinese) [卞保民, 赖小明, 杨玲, 李振华, 贺安之 2012 物理学报 61 080401]

    [21]

    Yu Y Q 1997 Introduction of general relativity (Beijing: Peking University Press) p18, 133, 158 (in Chinese) [愈允强 1997 广义相对论引论 (北京:北京大学出版社) 第18, 133, 158页]

    [22]

    Zhu H, Ji C C 2011 Fractal theory and its applications (Beijing: Science Press) p23 (in Chinese)[朱华, 姬翠翠 2011 分形理论及应用(北京:科学出版社) 第23页]

    [23]

    Yu Y Q 2002 Cosmophysics lectures (Beijing: Peking University Press) p104, 105, 214 (in Chinese)[俞允强 2002 物理宇宙学讲义(北京:北京大学出版社) 第104, 105, 214页]

  • [1] Liu Yin-Hua, Li Xiao-Hui. Super-high accurate new method of common-view time comparison based on space station. Acta Physica Sinica, 2018, 67(19): 190601. doi: 10.7498/aps.67.20180842
    [2] Shao Jian-Zhou, Wang Yong-Jiu. Acceleration effect in the gravitational field of black hole involving a global monopole. Acta Physica Sinica, 2012, 61(11): 110402. doi: 10.7498/aps.61.110402
    [3] Bian Bao-Min, Lai Xiao-Ming, Yang Ling, Li Zhen-Hua, He An-Zhi. Variable space scale factor spherical coordinates and time-space metric. Acta Physica Sinica, 2012, 61(8): 080401. doi: 10.7498/aps.61.080401
    [4] Xiang Mao-Huai, Chen Ju-Hua, Wang Yong-Jiu. Accretion and radiation in black hole with a global monopole. Acta Physica Sinica, 2011, 60(9): 090401. doi: 10.7498/aps.60.090401
    [5] Wang Yong-Jiu, Li Ai-Gen, Gong Tian-Xi, Chen Ju-Hua. A kind of singularity-free cosmology model. Acta Physica Sinica, 2010, 59(2): 712-715. doi: 10.7498/aps.59.712
    [6] Wu Ya-Bo, Deng Xue-Mei, Zhao Guo-Ming, Li Song, Lü Jian-Bo, Yang Xiu-Yi. Hyperbolic phase transformation group and its applicaton to four-dimensional relativistic spacetime. Acta Physica Sinica, 2005, 54(11): 4994-4998. doi: 10.7498/aps.54.4994
    [7] Guo Han-Ying, Huang Chao-Guang, Tian Yu, Xu Zhan, Zhou Bin. Beltrami-de Sitter spacetime and de Sitter invariant special relativity. Acta Physica Sinica, 2005, 54(6): 2494-2504. doi: 10.7498/aps.54.2494
    [8] Chen Guang. A non-collapsing solution of a uniform-density ball of dust in the discrete spacetime. Acta Physica Sinica, 2005, 54(7): 2971-2976. doi: 10.7498/aps.54.2971
    [9] Li Zong-Cheng. Spatiotemporal relation of prolongable general relativity in the irreversible process of a dissipative system. Acta Physica Sinica, 2003, 52(4): 767-773. doi: 10.7498/aps.52.767
    [10] WANG YONG-JIU, TANG ZHI-MING. THE STABILITY OF A KIND OF COSMOLOGICAL MODEL. Acta Physica Sinica, 2001, 50(10): 1829-1832. doi: 10.7498/aps.50.1829
    [11] ZHONG MING-QIAN. ESTIMATION OF POST-NEWTONIAN APPROXIMATION OF GRAVITY THAT AFFECTS SATELLITES OF PLANET. Acta Physica Sinica, 2001, 50(12): 2497-2500. doi: 10.7498/aps.50.2497
    [12] TANG ZHI-MING, WANG YONG-JIU. RADIATING OF ACCELERATING CHARGE IN GENERAL RELATIVITY. Acta Physica Sinica, 1999, 48(4): 561-565. doi: 10.7498/aps.48.561
    [13] ZHAO REN, LIU LIAO. THE REACTION TO THE SCHWARZSCHILD SPACE-TIME BY THE HAWKING EVAPORATION. Acta Physica Sinica, 1998, 47(12): 2074-2078. doi: 10.7498/aps.47.2074
    [14] TAO BI-XIU, TAO BI-YOU. GENERAL-RELATIVISTIC “WALL OF GALAXIES”. Acta Physica Sinica, 1996, 45(7): 1091-1099. doi: 10.7498/aps.45.1091
    [15] Duan Yi-Shi, Feng Shi-Xiang. . Acta Physica Sinica, 1995, 44(9): 1373-1381. doi: 10.7498/aps.44.1373
    [16] CUI SHI-ZHI. EXPECTATION TO THE TEST IN BEIJING FOR ANISOTROPY OF THE LIGHT VELOCITY (ON GENERAL RELATIVITY AND METRIC THEORIES). Acta Physica Sinica, 1989, 38(11): 1882-1885. doi: 10.7498/aps.38.1882
    [17] Huang Chao-guang, Wang Yong-cheng. SPACE-TIME STRUCTURE OF THE SUPERPOSITION OF TWO CO-LINEAR KERR BLACK HOLES'METRICS. Acta Physica Sinica, 1986, 35(10): 1322-1329. doi: 10.7498/aps.35.1322
    [18] Liu Wen-sen. LOCALISATION OF ENERGY IN GENERAL RELATIVITY. Acta Physica Sinica, 1983, 32(4): 515-519. doi: 10.7498/aps.32.515
    [19] ZHU SI-CHANG. GRAVITATIONAL MASS DEFECT AND ROTATIONAL MASS EFFECT FOR A ROTARY SOLID SPHERE IN GENERAL THEORY OF RELATIVITY. Acta Physica Sinica, 1979, 28(6): 894-900. doi: 10.7498/aps.28.894
    [20] GUO HAN-YING, WU YONG-SHI, LI GEN-DAO. THE SPINOR FORMALISM AND THE COMPLEX-VECTOR FORMALISM OF GENERAL RELATIVITY. Acta Physica Sinica, 1974, 23(5): 5-16. doi: 10.7498/aps.23.5
Metrics
  • Abstract views:  6076
  • PDF Downloads:  469
  • Cited By: 0
Publishing process
  • Received Date:  07 January 2012
  • Accepted Date:  23 February 2012
  • Published Online:  05 September 2012

/

返回文章
返回