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Student Number 87222031
Author Kuai-Hong Vu(­J¶Q¶¯)
Author's Email Address No Public.
Statistics This thesis had been viewed 1664 times. Download 621 times.
Department Physics
Year 1999
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title Quasilocal Energy-Momentum and Angular Momentum for Teleparallel Gravity
Date of Defense 2000-07-05
Page Count 58
Keyword
  • Energy and angular momentum
  • Quasilocal
  • Teleparallel
  • Abstract A new quasilocal energy expression for conserved quantities, energy and angular momentum, is obtained from the covariant Hamiltonian formulation of metric compatible teleparallel GR. The field equations and one of the quasilocal expressions obtained from our approach turn out to be equivalent to those of usual Riemannian description of GR. We tested our expressions by evaluating them for the Kerr solution without
    cosmological constant and found them to give the correct total value for energy and angular momentum asymptotically. Our result shows that contrary to Moller's expectation the
    teleparallel formulation is no better than the Riemannian description in providing for a good localization of energy-momentum and angular momentum.
    Table of Content 1.Introduction
    1.1 Gravitational energy-momentum and its localization
    1.2 Teleparallel theory
    1.3 Outline of this thesis
    2. Teleparallel Lagrangian and Hamiltonian formulation
    2.1 Introduction
    2.2 Usual Lagrangian and Hamiltonian formulation
    2.3 Formulation with Lagrange multiplier method
    2.3.1 General formulation for geometric dynamic theories
    2.3.2 Formulation for standard Einstein-Hilbert Lagrangian
    3. Non-uniqueness
    3.1 One solution for the Lagrange multiplier
    3.2 Non-unique Lagrange multiplier
    4. Evaluation of energy and angular momentum for Kerr solution
    4.1 Calculation with five types of coframes
    4.2 Discussion fo this result
    4.3 Comparison with other's expression
    5. Conclusion
    A Calculation of energy and angular momentum for Kerr solution in detail
    Reference 1. Misner C W, Thorne K S and Wheeler J A 1973 Gravitation
    2. Chen C M 1994 Quasilocal quantities for gravity theories MSc Thesis National Central University, Chungli unpublished
    3. Chiang-Mei Chen and James M Nester 1999 Class. Quantum Grav. 16 1279-1304
    4. Nester J M 1991 Mod. Phys. Lett. A 6 2655-61
    5. Nester J M 1984 The gravitational Hamiltonian Asymptotic Behavior of Mass and Space-Time Geometry (Lecture Notes in Physics vol 202) ed F Flaherty (Berlin: Springer) pp 155-63
    6. Regge T and Teitelboim C 1974 Ann. Phys. 88 286-319
    7. Kijowski J and Tulczyjew W M 1979 A Symplectic Framework for Field Theories (Lecture Notes in Physics vol 107) (Berlin: Springer)
    8. Y-S. Duan, J-C. Liu and X-G. Dong, ¡§General Covariant Energy-Momentum Conservation Law in General Spacetime¡¨, Gen. Rel. Grav. 20 (1988) 485-496
    9. Y-S. Duan and S-S. Feng, ¡§General Covariant Conservation Law of Angular Momentum in General Relativity¡¨, Comm. Theor. Phys. 25 (1996) 99-104.
    10. C. Mo ller, symbol92 On the Localization of the energy of a Physical System in the General Theory of Relativity", Ann. Phys. 4 (1958) 347-371.
    11. R. Weitzenbock, Invariantentheorie (Noordhoff, Gronningen, 1923).
    12. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. 217 (1928).
    13. K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979).
    14. J. A. Schouten, Ricci Calculus, 2nd ed. (Springer-Verlag, London, 1954).
    15. J. M. Nester and H. J. Yo ¡§Symmetric teleparallel general relativity¡¨, Chin. J. Phys. 37 113-117 (1999).
    16. J. M. Nester ¡§Positive energy via the teleparallel Hamiltonian¡¨ Int. J. Mod. Phys. A 4 (1989) 1755-1772.
    17. J. David Brown and J. W. York, Jr., Phys. Rev. D 47 ,1407 (1993).
    18. Arnowitt R, Deser S and Misner C W 1962 The dynamics of general relativity Gravitation: an Introduction to Current Research ed. L Witten (New York: Wiley) pp 227-65.
    19. V. C. de Andrade, L. C. T. Guillen and J. G. Pereia ¡§Gravitational Energy-Momentum Density in Teleparallel Gravity¡¨ Phys. Rev. Lett. 84 (2000) 4533-4536
    20. C. Mo ller, ¡§Conservation Laws and Absolute Parallelism in General Relativity¡¨, Mat. Fys. Dan. Vid. Selsk. 1 (1961) 1-50.
    Advisor
  • James M. Nester(¿´µ¯S)
  • Files
  • 87222031.pdf
  • approve immediately
    Date of Submission 2000-07-05

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