Numerical Relativity : Solving Einstein's Equations on the Computer
Thomas W. Baumgarte
Bok Engelsk 2010 · Electronic books.
| Utgitt | Cambridge : Cambridge University Press , 2010
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| Omfang | 1 online resource (718 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Half-title; Title; Copyright; Contents; Preface; What is numerical relativity?; About this book; Suggestions for using this book; 1 General relativity preliminaries; 1.1 Einstein's equations in 4-dimensional spacetime; Cast of characters; Geodesics; The Einstein field equations; Gravitational radiation; 1.2 Black holes; Schwarzschild black holes; Kerr black holes; Global theorems; 1.3 Oppenheimer-Volkoff spherical equilibrium stars; Polytropes; 1.4 Oppenheimer-Snyder spherical dust collapse; 2 The 3+1 decompostion of Einstein's equations; 2.1 Notation and conventions. - 2.2 Maxwell's equations in Minkowski spacetime2.3 Foliations of spacetime; 2.4 The extrinsic curvature; 2.5 The equations of Gauss, Codazzi and Ricci; 2.6 The constraint and evolution equations; 2.7 Choosing basis vectors: the ADM equations; 3 Constructing initial data; 3.1 Conformal transformations; 3.1.1 Conformal transformation of the spatial metric; 3.1.2 Elementary black hole solutions; 3.1.3 Conformal transformation of the extrinsic curvature; 3.2 Conformal transverse-traceless decomposition; A spinning black hole; A boosted black hole; 3.3 Conformal thin-sandwich decomposition. - 3.4 A step further: the ``waveless'' approximation3.5 Mass, momentum and angular momentum; 4 Choosing coordinates: the lapse and shift; 4.1 Geodesic slicing; 4.2 Maximal slicing and singularity avoidance; 4.3 Harmonic coordinates and variations; 4.4 Quasi-isotropic and radial gauge; 4.5 Minimal distortion and variations; 5 Matter sources; 5.1 Vacuum; 5.2 Hydrodynamics; 5.2.1 Perfect gases; Wilson scheme; High-resolution shock-capturing (HRSC) schemes; Smoothed particle hydrodynamics (SPH) schemes; Rankine-Hugoniot conditions; Tests; 5.2.2 Imperfect gases; Heat and radiation diffusion. - 5.2.3 Radiation hydrodynamics5.2.4 Magnetohydrodynamics; Electromagnetic field equations; Equations of baryon, energy and momentum conservation; Tests; 5.3 Collisionless matter; Particle methods; Phase space methods; 5.4 Scalar fields; 6 Numerical methods; 6.1 Classification of partial differential equations; 6.2 Finite difference methods; 6.2.1 Representation of functions and derivatives; 6.2.2 Elliptic equations; 6.2.3 Hyperbolic equations; 6.2.4 Parabolic equations; 6.2.5 Mesh refinement; 6.3 Spectral methods; 6.3.1 Representation of functions and derivatives; 6.3.2 A simple example. - 6.3.3 Pseudo-spectral methods with Chebychev polynomials6.3.4 Elliptic equations; 6.3.5 Initial value problems; 6.3.6 Comparison with finite-difference methods; 6.4 Code validation and calibration; 7 Locating black hole horizons; 7.1 Concepts; 7.2 Event horizons; 7.3 Apparent horizons; 7.3.1 Spherical symmetry; 7.3.2 Axisymmetry; 7.3.3 General case: no symmetry assumptions; 7.4 Isolated and dynamical horizons; 8 Spherically symmetric spacetimes; Choices! Choices!; 8.1 Black holes; Familiar gauge choices; Maximal slicing; 8.2 Collisionless clusters: stability and collapse. - 8.2.1 Particle method. - Pedagogical introduction to numerical relativity for students and researchers entering the field, and interested scientists.
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| Emner | |
| Sjanger | |
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| ISBN | 9780521514071
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