廣義相對論的3+1形式——數值相對論基礎(英文影印版) epub pdf mobi txt 電子書 下載 2024
發表於2024-11-11
廣義相對論的3+1形式——數值相對論基礎(英文影印版) epub pdf mobi txt 電子書 下載 2024
基本信息
書名:廣義相對論的3+1形式——數值相對論基礎(英文影印版)
原價:54.00元
作者:(法)古爾古隆
齣版社:北京大學齣版社
齣版日期:2014-10-01
ISBN:9787301248317
字數:376000
頁碼:294
版次:1
裝幀:平裝
開本:16開
商品重量:0.4kg
編輯推薦
盡管物理學傢提齣瞭一些新理論,但相對論目前依然是唯一成熟的現代引力理論。而對於相對論的研究也遠遠沒有走到盡頭,其豐富內涵依然有待發掘。《廣義相對論的3 1形式》講述瞭相對論的基本理論和數值方法的基礎。對於從事或有誌於從事相對論研究的研究人員或研究生,本書都是不可錯過的傑作。
內容提要
《廣義相對論的3 1形式》詳細地講解瞭3 1形式的廣義相對論和數值相對論基礎。本書從研究相對論所必備的數學工具,如微分幾何、超麯麵的嵌入等講起,逐步引入瞭愛因斯坦方程、物質和電磁場方程等的3 1分解。之後,通過更高等的數學工具,如共形變換等,討論瞭現代相對論的一些重要問題。
目錄
1 Introduction References2 Basic Differential Geometry 2.1 Introduction 2.2 Differentiable Manifolds 2.2.1 Notion of Manifold 2.2.2 Vectors on a Manifold 2.2.3 Linear Forms 2.2.4 Tensors 2.2.5 Fields on a Manifold 2.3 Pseudo-Riemannian Manifolds 2.3.1 Metric Tensor 2.3.2 Signature and Orthonormal Bases 2.3.3 Metric Duality 2.3.4 Levi-Civita Tensor 2.4 Covariant Derivative 2.4.1 Affine Connection on a Manifold 2.4.2 Levi-Civita Connection 2.4.3 Curvature 2.4.4 Weyl Tensor 2.5 Lie Derivative 2.5.1 Lie Derivative of a Vector Field 2.5.2 Generalization to Any Tensor Field References3 Geometry of Hypersurfaees 3.1 Introduction 3.2 Framework and Notations 3.3 Hypersurface Embedded in Spacetime 3.3.1 Definition 3.3.2 Normal Vector 3.3.3 Intrinsic Curvature 3.3.4 Extrinsic Curvature 3.3.5 Examples: Surfaces Embedded in the Euclidean Space R3 3.3.6 An Example in Minkowski Spacetime: The Hyperbolic Space H3 3.4 Spacelike Hypersurfaces 3.4.1 The Orthogonal Projector 3.4.2 Relation Between K and Vn 3.4.3 Links Between the ▽ and D Connections 3.5 Gauss-Codazzi Relations 3.5.1 Gauss Relation 3.5.2 Codazzi Relation References4 Geometry of Foliations 4.1 Introduction 4.2 Globally Hyperbolic Spacetimes and Foliations 4.2.1 Globally Hyperbolic Spacetimes 4.2.2 Definition of a Foliation 4.3 Foliation Kinematics 4.3.1 Lapse Function 4.3.2 Normal Evolution Vector 4.3.3 Eulerian Observers 4.3.4 Gradients of n and m 4.3.5 Evolution of the 3-Metric 4.3.6 Evolution of the Orthogonal Projector 4.4 Last Part of the 3 1 Deposition of the Riemann Tensor. 4.4.1 Last Non Trivial Projection of the Spacetime Riemann Tensor 4.4.2 3 1 Expression of the Spacetime Scalar Curvature. References5 3 1 Deposition of Einstein Equation 5.1 Einstein Equation in 3 1 form 5.1.1 The Einstein Equation 5.1.2 3 1 Deposition of the Stress-Energy Tensor .. 5.1.3 Projection of the Einstein Equation 5.2 Coordinates Adapted to the Foliation 5.2.1 Definition 5.2.2 Shift Vector 5.2.3 3 1 Writing of the Metric Components 5.2.4 Choice of Coordinates via the Lapse and the Shift 5.3 3 1 Einstein Equation as a PDE System 5.3.1 Lie Derivatives Along m as Partial Derivatives 5.3.2 3 1 Einstein System 5.4 The Cauchy Problem 5.4.1 General Relativity as a Three-Dimensional Dynamical System 5.4.2 Analysis Within Gaussian Normal Coordinates 5.4.3 Constraint Equations 5.4.4 Existence and Uniqueness of Solutions to the Cauchy Problem 5.5 ADM Hamiltonian Formulation 5.5.1 3 1 form of the Hilbert Action 5.5.2 Hamiltonian Approach References6 3 1 Equations for Matter and Electromagic Field 6.1 Introduction 6.2 Energy and Momentum Conservation 6.2.1 3 1 Deposition of the 4-Dimensional Equation 6.2.2 Energy Conservation 6.2.3 Newtonian Limit 6.2.4 Momentum Conservation 6.3 Perfect Fluid 6.3.1 Kinematics 6.3.2 Baryon Number Conservation 6.3.3 Dynamical Quantities 6.3.4 Energy Conservation Law 6.3.5 Relativistic Euler Equation 6.3.6 Flux-Conservative Form 6.3.7 Further Developments 6.4 Electromagism 6.4.1 Electromagic Field 6.4.2 3 1 Maxwell Equations 6.4.3 Electromagic Energy, Momentum and Stress... 6.5 3 1 Ideal Magohydrodynamics 6.5.1 Basic Settings 6.5.2 Maxwell Equations 6.5.3 Electromagic Energy, Momentum and Stress... 6.5.4 MHD-Euler Equation 6.5.5 MHD in Flux-Conservative Form References7 Conformal Deposition 7.1 Introduction 7.2 Conformal Deposition of the 3-Metric 7.2.1 Unit-Determinant Conformal 'Metric' 7.2.2 Background Metric 7.2.3 Conformal Metric 7.2.4 Conformal Connection 7.3 Expression of the Ricci Tensor 7.3.1 General Formula Relating the Two Ricci Tensors 7.3.2 Expression in Terms of the Conformal Factor 7.3.3 Formula for the Scalar Curvature 7.4 Conformal Deposition of the Extrinsic Curvature 7.4.1 Traceless Deposition 7.4.2 Conformal Deposition of the Traceless Part 7.5 Conformal Form of the 3 1 Einstein System 7.5.1 Dynamical Part of Einstein Equation 7.5.2 Hamiltonian Constraint 7.5.3 Momentum Constraint 7.5.4 Summary: Conformal 3 1 Einstein System 7.6 Isenberg-Wilson-Mathews Approximation to General Relativity References8 Asymptotic Flatness and Global Quantifies 8.1 Introduction 8.2 Asymptotic Flatness 8.2.1 Definition 8.2.2 Asymptotic Coordinate Freedom 8.3 ADM Mass 8.3.1 Definition from the Hamiltonian Formulation of GR 8.3.2 Expression in Terms of the Conformal Deposition 8.3.3 Newtonian Limit 8.3.4 Positive Energy Theorem 8.3.5 Constancy of the ADM Mass 8.4 ADM Momentum 8.4.1 Definition 8.4.2 ADM 4-Momentum 8.5 Angular Momentum 8.5.1 The Supertranslation Ambiguity 8.5.2 The 'Cure'. 8.5.3 ADM Mass in the Quasi-Isotropic Gauge 8.6 Komar Mass and Angular Momentum 8.6.1 Komar Mass 8.6.2 3 1 Expression of the Komar Mass and Link with the ADM Mass 8.6.3 Komar Angular Momentum References9 The Initial Data Problem 9.1 Introduction 9.1.1 The Initial Data Problem 9.1.2 Conformal Deposition of the Constraints 9.2 Conformal Transverse-Traceless Method 9.2.1 Longitudinal / Transverse Deposition of A ij 9.2.2 Conformal Transverse-Traceless Form of the Constraints 9.2.3 Decoupling on Hypersurfaces of Constant Mean Curvature 9.2.4 Existence and Uniqueness of Solutions to Lichnerowicz Equation 9.2.5 Conformally Flat and Momentarily Static Initial Data 9.2.6 Bowen-York Initial Data 9.3 Conformal Thin Sandwich Method 9.3.1 The Original Conformal Thin Sandwich Method . 9.3.2 Extended Conformal Thin Sandwich Method 9.3.3 XCTS at Work: Static Black Hole Example 9.3.4 Uniqueness Issue 9.3.5 Comparing CTT, CTS and XCTS 9.4 Initial Data for Binary Systems 9.4.1 Helical Symmetry 9.4.2 Helical Symmetry and IWM Approximation 9.4.3 Initial Data for Orbiting Binary Black Holes 9.4.4 Initial Data for Orbiting Binary Neutron Stars 9.4.5 Initial Data for Black Hole: Neutron Star Binaries. References10 Choice of Foliation and Spatial Coordinates 10.1 Introduction 10.2 Choice of Foliation 10.2.1 Geodesic Slicing 10.2.2 Maximal Slicing 10.2.3 Harmonic Slicing 10.2.4 1 log Slicing 10.3 Evolution of Spatial Coordinates 10.3.1 Normal Coordinates 10.3.2 Minimal Distortion 10.3.3 Approximate Minimal Distortion 10.3.4 Gamma Freezing 10.3.5 Gamma Drivers 10.3.6 Other Dynamical Shift Gauges 10.4 Full Spatial Coordinate-Fixing Choices 10.4.1 Spatial Harmonic Coordinates 10.4.2 Dirac Gauge References11 Evolution schemes 11.1 Introduction 11.2 Constrained Schemes 11.3 Free Evolution Schemes 11.3.1 Definition and Framework 11.3.2 Propagation of the Constraints 11.3.3 Constraint-Violating Modes 11.3.4 Symmetric Hyperbolic Formulations 11.4 BSSN Scheme 11.4.1 Introduction 11.4.2 Expression of the Ricci Tensor of the Conformal Metric 11.4.3 Reducing the Ricci Tensor to a Laplace Operator 11.4.4 The Full Scheme 11.4.5 Applications ReferencesAppendix A: Conformal Killing Operator and Conformal Vector LaplacianAppendix B: Sage CodesIndex
作者介紹
古爾古隆(E. Gourgoulhon),法國LUTh教授。
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廣義相對論的3+1形式——數值相對論基礎(英文影印版) epub pdf mobi txt 電子書 下載 2024
廣義相對論的3+1形式——數值相對論基礎(英文影印版) 下載 epub mobi pdf txt 電子書廣義相對論的3+1形式——數值相對論基礎(英文影印版) mobi pdf epub txt 電子書 下載 2024
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廣義相對論的3+1形式——數值相對論基礎(英文影印版) epub pdf mobi txt 電子書 下載 2024