rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: 3+1 Formalism in General Relativity
    sub title: Bases of Numerical Relativity
  name:
    name part: Gourgoulhon, Eric.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVII, 294 p. 29 illus. online resource.
  abstract: 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 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.
  table of contents: Basic 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.
  note: by Eric Gourgoulhon.
  subject:
    topic: Physics
  subject:
    topic: Computer mathematics
  subject:
    topic: Gravitation
  subject:
    topic: Astronomy
  subject:
    topic: Astrophysics
  subject:
    topic: Cosmology
  subject:
    topic: Physics
  subject:
    topic: Numerical and Computational Physics
  subject:
    topic: Classical and Quantum Gravitation, Relativity Theory
  subject:
    topic: Astronomy, Astrophysics and Cosmology
  subject:
    topic: Computational Mathematics and Numerical Analysis
  classification: QC1-999
  classification: 530.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Physics, 846
  identifier: 9783642245251
  identifier: http://dx.doi.org/10.1007/978-3-642-24525-1
  record info:
    record creation date: 120227
    record change date: 20151123143611.0
    record identifier: 978-3-642-24525-1