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	COVER
	VERSUS
	TITLE PAGE
	INDEX CARD
	APPROVAL TERM
	DEDICATORY
	ACKNOWLEDGEMENTS
	ABSTRACT
	RESUMO
	LIST OF FIGURES
	LIST OF ABBREVIATIONS
	LIST OF SYMBOLS
	CONTENTS
	1 INTRODUCTION
	2 LINEAR REGIME OF THE EINSTEIN'S FIELD EQUATIONS AND GRAVITATIONAL WAVES
	2.1 First Order Perturbations
	2.2 Higher Order Perturbations
	2.3 Green's Functions for the Flat Background and Perturbations of First Order
	2.4 Multipolar Expansion
	2.5 Gravitational Radiation from Point Particle Binary System
	3 THE Eth FORMALISM AND THE SPIN-WEIGHTED SPHERICAL HARMONICS 
	3.1 Non-conformal Mappings in the Sphere
	3.2 Stereographic Coordinates
	3.3 Decomposition of the Metric of the Unit Sphere
	3.4 Transformation Rules for Vectors and One-forms
	3.5 Transformation Rules for the Dyads and Spin-weight
	3.6 Spin-weighted Scalars and Spin-weight
	3.7 Raising and Lowering Operators
	3.8 Transforming the Coordinate Basis
	3.9 Legendrian Operator
	3.10 The and in Spherical Coordinates
	3.11 Integrals for the Angular Manifold
	3.12 Spin-weighted Spherical Harmonics sYlm
	3.13 Spin-weighted Spherical Harmonics sZlm
	4 THE INITIAL VALUE PROBLEM AND THE NON-LINEAR REGIME OF THE EINSTEIN'S FIELD EQUATIONS
	4.1 The Initial Value Problem
	4.2 Arnowitt-Desser-Misner Formulations (ADM)
	4.2.1 (ADM) formalism
	4.2.2 The Baumgarte-Shibata-Shapiro-Nakamura (BSSN) Equations
	4.3 Outgoing Characteristic Formulation
	4.3.1 The Bondi-Sachs Metric
	4.3.2 Characteristic Initial Value Problem
	4.3.3 The Einstein's Field Equations
	4.4 The Einstein's Field Equations in the Quasi-Spherical Approxi-mation
	4.5 The Einstein's Field equations Using the Eth Formalism
	5 LINEAR REGIME IN THE CHARACTERISTIC FORMULA- TION AND THE MASTER EQUATION SOLUTIONS
	5.1 Einstein's Field Equations in the linear 
	5.2 Harmonic Decomposition and Boundary Problem
	5.3 The Master Equation
	5.4 Families of Solutions to the Master Equation
	5.4.1 The Minkowski's Background
	5.4.2 The Schwarzschild's Background
	5.5 Families of Solutions for l=2
	5.6 Thin Shell
	6 APPLICATIONS
	6.1 Point Particle Binary System with Different Masses
	6.1.1 Gravitational Radiation from the Binary System
	6.2 Eccentric Point Particle Binary System
	6.2.1 Gravitational Radiation Emitted by the Binary
	7 CONCLUSIONS, FINAL REMARKS AND PERSPECTIVES
	REFERENCES
	 Appendix A - Explicit Form for the and Operators in Stereographic Coordinates
	 Appendix B - Angular Operators , and in terms of and

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