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Table of Contents
Intro; Supervisor's Foreword; Abstract; Acknowledgements; Contents; Nomenclature; Part I Background Material; 1 Introduction; 1.1 General Relativity; 1.1.1 General Covariance; 1.1.2 The Equivalence Principle; 1.1.3 Consequences of GR; 1.2 Numerical Relativity; 1.2.1 NR as a Cauchy Problem; 1.2.2 Key Historical Developments in NR; 1.2.3 Existing Numerical Codes and AMR; 1.3 Scalar Fields with Gravity; 1.3.1 Scalar Fields and Scalar Potentials; 1.3.2 Scalar Fields in Cosmology; 1.3.3 Critical Collapse of Scalar Fields; References; 2 Technical Background; 2.1 GR
Key Theoretical Concepts
2.1.1 Geometric Preliminaries2.1.2 The Einstein Equation from Geometric Principles; 2.1.3 The Einstein Equation from Action Principles; 2.2 NR
Key Theoretical Concepts; 2.2.1 ADM Decomposition; 2.2.2 Numerical Stability; 2.2.3 Initial Conditions, Gauge Choice and Interpretation of Results; 2.3 Scalar Fields with Gravity; 2.3.1 Scalar Matter with Minimal Coupling; 2.3.2 Early Universe Cosmology; 2.3.3 Critical Collapse; References; Part II Code Development Work; 3 GRChombo
Code Development and Testing; 3.1 Features of Chombo; 3.1.1 Chombo Structure and Classes
3.1.2 Berger-Rigoutsos Block-Structured AMR3.1.3 Load Balancing; 3.2 Implementing GRChombo; 3.2.1 Evolution Equations; 3.2.2 Discretization and Time-Stepping; 3.2.3 Kreiss-Oliger Dissipation; 3.2.4 Boundary Conditions; 3.2.5 Initial Conditions; 3.2.6 Apparent Horizon Finder in Spherical Symmetry; 3.2.7 Extracting ADM Mass and Momenta; 3.2.8 Gravitational Wave Detection; 3.3 Testing GRChombo; 3.3.1 Apples with Apples Tests; 3.3.2 Vacuum Black Hole Spacetimes; 3.3.3 Choptuik Scalar Field Collapse; 3.3.4 Convergence Test: Head on Collision of Two Black Holes; 3.3.5 MPI Scaling Properties
3.3.6 Performance ComparisonReferences; Part III Research Work; 4 Inhomogeneous Inflation; 4.1 Introduction; 4.2 Theory and Methodology; 4.2.1 Initial Conditions; 4.2.2 Numerical Set-Up; 4.3 Small Field Inflation; 4.3.1 Small Field Model with Extended Flat Direction; 4.3.2 Pull Back Effects in Small Field Inflation; 4.3.3 Small Field Model Without Extended Flat Direction; 4.4 Large Field Inflation; 4.4.1 Large Field Inflation with Constant K; 4.4.2 Can Black Holes Stop Inflation?; 4.4.3 Large Field Inflation with Spatially Varying K; 4.5 Conclusions; 4.5.1 Robustness of Small Field Inflation
4.5.2 Robustness of Large Field InflationReferences; 5 Critical Bubble Collapse; 5.1 Introduction; 5.2 Methodology; 5.2.1 Gauge Conditions; 5.2.2 Initial Data; 5.2.3 Resolution and Convergence; 5.3 Spherical Symmetry; 5.3.1 Spherical Symmetry in 1+1D; 5.3.2 Spherical Symmetry in 3+1D; 5.4 Beyond Spherical Symmetry
3 + 1D Simulations; 5.4.1 Radial Perturbations of a Spherical Bubble
Axisymmetric Bubbles; 5.4.2 Amplitude Perturbations of a Spherical Subble
Asymmetric Bubbles; 5.5 Discussion; References; Part IV Conclusions; 6 Conclusions and Further Work; 6.1 Development of GRChombo
Key Theoretical Concepts
2.1.1 Geometric Preliminaries2.1.2 The Einstein Equation from Geometric Principles; 2.1.3 The Einstein Equation from Action Principles; 2.2 NR
Key Theoretical Concepts; 2.2.1 ADM Decomposition; 2.2.2 Numerical Stability; 2.2.3 Initial Conditions, Gauge Choice and Interpretation of Results; 2.3 Scalar Fields with Gravity; 2.3.1 Scalar Matter with Minimal Coupling; 2.3.2 Early Universe Cosmology; 2.3.3 Critical Collapse; References; Part II Code Development Work; 3 GRChombo
Code Development and Testing; 3.1 Features of Chombo; 3.1.1 Chombo Structure and Classes
3.1.2 Berger-Rigoutsos Block-Structured AMR3.1.3 Load Balancing; 3.2 Implementing GRChombo; 3.2.1 Evolution Equations; 3.2.2 Discretization and Time-Stepping; 3.2.3 Kreiss-Oliger Dissipation; 3.2.4 Boundary Conditions; 3.2.5 Initial Conditions; 3.2.6 Apparent Horizon Finder in Spherical Symmetry; 3.2.7 Extracting ADM Mass and Momenta; 3.2.8 Gravitational Wave Detection; 3.3 Testing GRChombo; 3.3.1 Apples with Apples Tests; 3.3.2 Vacuum Black Hole Spacetimes; 3.3.3 Choptuik Scalar Field Collapse; 3.3.4 Convergence Test: Head on Collision of Two Black Holes; 3.3.5 MPI Scaling Properties
3.3.6 Performance ComparisonReferences; Part III Research Work; 4 Inhomogeneous Inflation; 4.1 Introduction; 4.2 Theory and Methodology; 4.2.1 Initial Conditions; 4.2.2 Numerical Set-Up; 4.3 Small Field Inflation; 4.3.1 Small Field Model with Extended Flat Direction; 4.3.2 Pull Back Effects in Small Field Inflation; 4.3.3 Small Field Model Without Extended Flat Direction; 4.4 Large Field Inflation; 4.4.1 Large Field Inflation with Constant K; 4.4.2 Can Black Holes Stop Inflation?; 4.4.3 Large Field Inflation with Spatially Varying K; 4.5 Conclusions; 4.5.1 Robustness of Small Field Inflation
4.5.2 Robustness of Large Field InflationReferences; 5 Critical Bubble Collapse; 5.1 Introduction; 5.2 Methodology; 5.2.1 Gauge Conditions; 5.2.2 Initial Data; 5.2.3 Resolution and Convergence; 5.3 Spherical Symmetry; 5.3.1 Spherical Symmetry in 1+1D; 5.3.2 Spherical Symmetry in 3+1D; 5.4 Beyond Spherical Symmetry
3 + 1D Simulations; 5.4.1 Radial Perturbations of a Spherical Bubble
Axisymmetric Bubbles; 5.4.2 Amplitude Perturbations of a Spherical Subble
Asymmetric Bubbles; 5.5 Discussion; References; Part IV Conclusions; 6 Conclusions and Further Work; 6.1 Development of GRChombo