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Student Number 942202031
Author Da-Sheng Kung(ÅǤj³Ó)
Author's Email Address etbigwin@yahoo.com.tw
Statistics This thesis had been viewed 1354 times. Download 561 times.
Department Physics
Year 2007
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title Asymptotic Flatness Preserving Transformations in SL(4,R) sigma-model
Date of Defense 2008-05-07
Page Count 54
Keyword
  • asymptotic flat
  • black ring
  • five dimensional black hole
  • R) sigma-model
  • SL(4
  • Abstract We give a systematic method to determine the asymptotic flatness preserving transformations
    in the three-dimensional SL(4,R)/SO(2, 2) sigma-model arising from a
    five-dimensional gravity coupled to a dilaton and a three-form field. The permitted
    transformations depend on the coordinate choices. By focusing on three cases,
    namely the Kaluza-Klein black hole, five-dimensional black hole and black ring, we
    find out all possible asymptotic flatness preserving transformations and apply them
    to generate charge from single rotating vacuum solutions.
    Table of Content 1 Introduction 1
    2 SL(4,R) Symmetry 4
    2.1 Sigma-model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
    2.2 Basic symmetry transformations . . . . . . . . . . . . . . . . . . . . . 7
    2.3 Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
    3 Asymptotic Flatness Preserving 13
    3.1 AFP condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
    3.2 Kaluza-Klein vacuum R3,1 ¡Ñ S1 . . . . . . . . . . . . . . . . . . . . . 15
    3.3 5D Minkowski R4,1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
    3.4 Ring coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
    4 Charged Kaluza-Klein Black Holes 21
    4.1 R1 − L1 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 22
    4.2 T2 + T3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 23
    4.3 R2 + L3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 23
    4.4 S2 + S3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
    4.5 R3 + L2 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 24
    4.6 R4 − L4 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 25
    5 Charged 5D Black Holes 26
    5.1 S3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
    5.2 R2 + L3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 28
    5.2.1 Physical quantity . . . . . . . . . . . . . . . . . . . . . . . . . 29
    5.2.2 An equivalent approach . . . . . . . . . . . . . . . . . . . . . 29
    6 Charged Ring Solutions 31
    6.1 Neutral black rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
    6.2 S3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
    6.3 R2 + L3 transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 34
    6.3.1 Physical quantity . . . . . . . . . . . . . . . . . . . . . . . . . 35
    6.3.2 An equivalent approach . . . . . . . . . . . . . . . . . . . . . 37
    7 Conclusion 39
    7.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
    7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
    Bibliography 41
    A Kaluza-Klein theory 43
    B Relations of gauge field components 45
    C Black Rings 46
    C.1 Ring coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
    C.2 Neutral black rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
    D Target-space potentials 52
    Reference Bibliography
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    T. Wolf, ¡§ G2 generating technique for minimal D=5 supergravity and black
    rings, ¡¨ hep-th/0708.2361v2.
    [2] C. M. Chen, D. V. Gal¡¦tsov and S. A. Sharakin, ¡§ Inverse dualization and nonlocal
    dualities between Einstein gravity and supergravities, ¡¨ Class. Quantum
    Grav. 19 (2002), 347-373.
    [3] C. M. Chen, D. V. Gal¡¦tsov, K. Maeda and S. A. Sharakin, ¡§ SL(4,R) generating
    symmetry in five−dimensional gravity coupled to dilaton and three−form,
    ¡¨ Phys. Lett. B453, 7 (1999), hep-th/9901130.
    [4] H. Elvang, ¡§ A charged rotating black ring, ¡¨ Phys. Rev. D 68, 124016 (2003).
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    [7] R. Emparan, ¡§ Rotating circular strings and infinite non − uniqueness of
    black rings, ¡¨ JHEP 03 (2004) 064.
    [8] V. Frolov, A. Zelnikov and U. Bleyer, ¡§ Charged rotating black holes from
    five-dimensional point of view, ¡¨ Ann. der Physik (Leipzig) 44 (1987), 371-
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    [9] S. Giusto and A. Saxena, ¡§ Stationary axisymmetric solutions of five
    dimensional gravity, ¡¨hep-th/0705.4484v2.
    [10] J. H. Horne and G. T. Horowitz, ¡§ Rotating dilaton black holes, ¡¨ Phys. Rev.
    D46 (1992), 1340-1346, hep-th/9203083.
    [11] W. Israel, Phys. Rev. 164 (1967) 1776. B. Carter, Phys. Rev. Lett. 26 (1971)
    331. D. C. Robinson, Phys. Rev. Lett. 34 (1975) 905.
    [12] R. C. Myers and M. J. Perry, ¡§ Black holes in higher dimensional space−times,
    ¡¨ Ann. Phys. 172 (1986) 304.
    [13] A. A. Pomeransky and R. A. Sen¡¦kov, ¡§ Black ring with two angular momenta,
    ¡¨ hep-th/0612005.
    Advisor
  • Chiang-Mei Chen(³¯¦¿±ö)
  • Files
  • 942202031.pdf
  • approve immediately
    Date of Submission 2008-05-23

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