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Testing General Relativity Through the Computation of Radiative Terms And TESTING GENERAL RELATIVITY THROUGH THE COMPUTATION OF RADIATIVE TERMS AND WITHIN THE NEUTRON STAR STRONG-FIELD REGIME by Alexander Saffer A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics MONTANA STATE UNIVERSITY Bozeman, Montana April 2019 ©COPYRIGHT by Alexander Saffer 2019 All Rights Reserved ii DEDICATION Dedicated to my family, who provided me with their unconditional love and support. iii ACKNOWLEDGEMENTS I would like to acknowledge the hard work of my advisor Dr. Nicolás Yunes, whose dedication and compassion for physics and those in this field has taught me more than classes ever could. I would also like to thank the Dr. Kent Yagi and Dr. Hector Okada da Silva for their willingness to always help me no matter what I asked and for having the patience to put up with me whenever I struggled. In addition, I would like to thank Dr. Neil Cornish and the rest of the eXtreme Gravity Institute for providing an environment conducive to success. Lastly, I would like to thank my family and friends both within and outside of the MSU physics department who provided their support and guidance over these past 6 years, especially Meg. iv TABLE OF CONTENTS 1. INTRODUCTION ................................................................................................ 1 2. THE GRAVITATIONAL WAVESTRESS-ENERGY (PSEUDO)-TENSOR IN MODIFIED GRAVITY ...................................................................................12 Contribution of Authors and Co-Authors...............................................................12 Manuscript Information Page................................................................................13 Abstract ..............................................................................................................14 Introduction ........................................................................................................15 General Relativity................................................................................................18 Perturbed Action Method .............................................................................18 Perturbed Field Equation Method .................................................................22 Landau-Lifshitz Method...............................................................................24 Noether Current Method ..............................................................................26 Derivation of Physical Quantities: E˙ and P˙ ...................................................29 Jordan-Fierz-Brans-Dicke Theory.........................................................................30 Perturbed Action Method .............................................................................31 Perturbed Field Equation Method .................................................................34 Landau-Lifshitz Method...............................................................................35 Noether Current Method ..............................................................................36 Derivation of Physical Quantities: E˙ and P˙ ...................................................37 Einstein-Æther Theory.........................................................................................38 Perturbed Action Method .............................................................................41 Perturbed Field Equation Method .................................................................44 Landau-Lifshitz Method...............................................................................47 Noether Current Method ..............................................................................49 Derivation of Physical Quantities: E˙, P˙, and L˙ ..............................................52 Conclusion..........................................................................................................53 3. ANGULAR MOMENTUM LOSS FOR A BINARY SYSTEM IN EINSTEIN-ÆTHER THEORY.............................................................................56 Contribution of Authors and Co-Authors...............................................................56 Manuscript Information Page................................................................................57 Abstract ..............................................................................................................58 Introduction ........................................................................................................58 Einstein-Æther Theory.........................................................................................60 Gravitational Action ....................................................................................62 Matter Action..............................................................................................63 Field Equations ...........................................................................................64 v TABLE OF CONTENTS – CONTINUED Field Decomposition....................................................................................65 Angular Momentum Loss Rate.............................................................................68 General Calculation .....................................................................................68 Specialization to an N-Body System .............................................................71 Binary Dynamics in Æ-theory ..............................................................................74 Conclusion and Future .........................................................................................78 Acknowledgments................................................................................................79 4. THE EXTERIOR SPACETIME OF RELATIVISTIC STARS IN SCALAR- GAUSS-BONNET GRAVITY ..............................................................................80 Contribution of Authors and Co-Authors...............................................................80 Manuscript Information Page................................................................................81 Abstract ..............................................................................................................82 Introduction ........................................................................................................82 Scalar Gauss-Bonnet gravity ................................................................................85 Action.........................................................................................................85 Field equations ............................................................................................88 Perturbative expansion for the metric and fluid variables ................................89 Perturbative expansion of the field equations .................................................90 Solutions of the field equations outside the star......................................................92 O α¯ 0 equations.........................................................................................92 O α¯ 1 equations.........................................................................................93 O α¯ 2 equations.........................................................................................94 Comparison with black holes spacetimes.......................................................96 Solutions of the field equations inside the star........................................................97 O α¯ 0 equations.........................................................................................97 O α¯ 1 equations.........................................................................................98 O α¯ 2 equations.......................................................................................100 Astrophysical applications..................................................................................103 Circular orbits around the star.....................................................................104 Modified Kepler’s Third Law .....................................................................106 Quasiperiodic oscillations ..........................................................................106 Light bending............................................................................................109 Conclusions and outlook ....................................................................................114 Addendum to sGB Work ....................................................................................116 On the maximum mass of the neutron star...................................................116 On the study of quasi-periodic orbits...........................................................118 vi TABLE OF CONTENTS – CONTINUED 5. CONCLUSION..................................................................................................121 REFERENCES CITED............................................................................................124 APPENDICES ........................................................................................................138 APPENDIX A : Brill-Hartle Averaging Scheme..................................................139 APPENDIX B : Electromagnetic Canonical SET ................................................142 APPENDIX C : Derivation of JFBD Reduced Field ............................................144 APPENDIX D : Expanded Action for Einstein-Æther ..........................................147 vii LIST OF
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