This 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 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....
|Title||:||3+1 Formalism in General Relativity: Bases of Numerical Relativity (Lecture Notes in Physics, Vol. 846)|
|Publisher||:||Springer 1st edition February 28, 2012|
|Number of Pages||:||294 pages|
|File Size||:||562 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
3+1 Formalism in General Relativity: Bases of Numerical Relativity (Lecture Notes in Physics, Vol. 846) Reviews
Excellent short book. Great derivations, very logical presentation. A great way to quickly get up to speed on 3+1 formulation of GR and be ready to read the literature and start working on simulations.
Everything OK !