臺灣博碩士論文加值系統

在此論文中，我們計算了Teleparallel Dark Energy Model下的Post-Newtonian Limit展開，重力場背景設定在Minkowski background。在此條件下，tetrad和Energy-Momentum tensor由此極限做弱場展開。最後，我們比較teleparallel gravity與廣義相對論的結果。

We calculate the post-Newtonian limit in the teleparallel equivalent of General Relativity
(TEGR) with a scalar eld which non-minimally couples to gravity. The background is set
up at Minkowski spacetime, and both the tetrad eld and energy momentum tensor are
perturbed in the parametrized post-Newtonian formalism. The comparisons of the post-
Newtonian result with general relativity and solar system experiments are discussed.

1 Introduction 1
2 Teleparallel Gravity 2
2.1 General Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Teleparallel Equivalent to General Relativity (TEGR) . . . . . . . . . . . . . 4
2.3 Teleparallel Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Method of Post-Newtonian Approximation 7
3.1 Newtonian Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Bookkeeping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Energy Momentum Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4 Post-Newtonian Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.5 Standard Post-Newtonian Gauge . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Perturbations in Teleparallel Gravity 16
4.1 Vierbein Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 Linear Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2.1 (0; 0) component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2.2 (i; j) component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2.3 (0; i) component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Post-Newtonian Limit of (0; 0) component . . . . . . . . . . . . . . . . . . . 23
4.4 Scalar Field Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Conclusions 28
Appendix 29
A The Torsion Square 30

[1] A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 217 (1928)
[2] F.W. Hehl, P. Von Der Heyde, G.D. Kerlick and J.M. Nester, Rev. Mod. Phys. 48, 393 (1976).
[3] K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979).
[4] E. E. Flanagan and E. Rosenthal, Phys. Rev. D 75, 124016 (2007).
[5] J. Garecki, arXiv:1010.2654 [gr-qc].
[6] C. -Q. Geng, C. -C. Lee, E. N. Saridakis and Y. -P. Wu, Phys. Lett. B 704, 384 (2011) [arXiv:1109.1092 [hep-th]].
[7] R. D. Reasenberg, I. I. Shapiro, P. E. MacNeil, R. B. Goldstein, J. C. Breidenthal, J. P. Brenkle, D. L. Cain and T. M. Kaufman et al., Astrophys. J. 234, L219 (1979).
[8] E. Fomalont, S. Kopeikin, G. Lanyi and J. Benson, Astrophys. J. 699, 1395 (2009) [arXiv:0904.3992 [astro-ph.CO]].
[9] B. Bertotti, L. Iess and P. Tortora, Nature 425, 374 (2003).
[10] S. Chandrasekhar, Astrophysical Journal, vol. 142, p.1488
[11] R. V. Wagoner, Phys. Rev. D 1, 3209 (1970).
[12] R. V. Wagoner and C. M. Will, Astrophys. J. 210, 764 (1976) [Erratum-ibid. 215, 984 (1977)]. 34
[13] C.M Will, Theory and Experiment in Gravitational Physics, revisited ed. (Cambridge University Press, Cambridge 1993).
[14] Weitzenbock, R.,Invariantentheories (P. Noordho, Groningen, 1923).