000 | 04153nam a22004935i 4500 | ||
---|---|---|---|
001 | 978-3-642-24525-1 | ||
003 | DE-He213 | ||
005 | 20190213151359.0 | ||
007 | cr nn 008mamaa | ||
008 | 120227s2012 gw | s |||| 0|eng d | ||
020 |
_a9783642245251 _9978-3-642-24525-1 |
||
024 | 7 |
_a10.1007/978-3-642-24525-1 _2doi |
|
050 | 4 | _aQC1-999 | |
072 | 7 |
_aPHU _2bicssc |
|
072 | 7 |
_aSCI040000 _2bisacsh |
|
072 | 7 |
_aPHU _2thema |
|
082 | 0 | 4 |
_a530.1 _223 |
100 | 1 |
_aGourgoulhon, Eric. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_a3+1 Formalism in General Relativity _h[electronic resource] : _bBases of Numerical Relativity / _cby Eric Gourgoulhon. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012. |
|
300 |
_aXVII, 294 p. 29 illus. _bonline resource. |
||
336 |
_atext _btxt _2rdacontent |
||
337 |
_acomputer _bc _2rdamedia |
||
338 |
_aonline resource _bcr _2rdacarrier |
||
347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes in Physics, _x0075-8450 ; _v846 |
|
505 | 0 | _aBasic Differential Geometry -- Geometry of Hypersurfaces -- Geometry of Foliations -- 3+1 decomposition of Einstein Equation -- 3+1 Equations for Matter and Electromagnetic Field -- Conformal Decompositon -- Asymptotic Flatness and Global Quantities -- The Initial Data Problem -- Choice of Foliation and Spatial Coordiinates -- Evolution Schemes -- Conformal Killing Operator and Conformal Vector Laplacian -- Sage Codes. | |
520 | _aThis graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book. | ||
650 | 0 | _aAstronomy. | |
650 | 0 |
_aComputer science _xMathematics. |
|
650 | 1 | 4 |
_aNumerical and Computational Physics, Simulation. _0http://scigraph.springernature.com/things/product-market-codes/P19021 |
650 | 2 | 4 |
_aClassical and Quantum Gravitation, Relativity Theory. _0http://scigraph.springernature.com/things/product-market-codes/P19070 |
650 | 2 | 4 |
_aAstronomy, Astrophysics and Cosmology. _0http://scigraph.springernature.com/things/product-market-codes/P22006 |
650 | 2 | 4 |
_aComputational Mathematics and Numerical Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M1400X |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642245244 |
776 | 0 | 8 |
_iPrinted edition: _z9783642245268 |
830 | 0 |
_aLecture Notes in Physics, _x0075-8450 ; _v846 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-642-24525-1 |
912 | _aZDB-2-PHA | ||
912 | _aZDB-2-LNP | ||
999 |
_c10477 _d10477 |