TitleGravitation as a plastic distortion of the Lorentz vacuum
Author(s)Virginia Velma Fern�andez;Waldyr A. Rodrigues;Jr
PublicationBerlin, Springer-Verlag, 2010.
Description1 online resource (x, 153 p.)
Contents NoteCover13; -- Gravitation as a Plastic Distortion of the Lorentz 13;Vacuum -- Preface -- Contents -- Chapter 1 Introduction -- 1.1 Geometrical Space Structures, Curvature, Torsion and Nonmetricity Tensors -- 1.2 Flat Spaces, Affine Spaces, Curvature and Bending -- 1.3 Killing Vector Fields, Symmetries and Conservation Laws -- References -- Chapter 2 Multiforms, Extensors, Canonical and Metric Clifford Algebras -- 2.1 Multiforms -- 2.1.1 The k-Part Operator and Involutions -- 2.1.2 Exterior Product -- 2.1.3 The Canonical Scalar Product -- 2.1.4 Canonical Contractions -- 2.2 The Canonical Clifford Algebra -- 2.3 Extensors -- 2.3.1 The Space extV -- 2.3.2 The Space (p, q)-extV of the (p, q)-Extensors -- 2.3.3 The Adjoint Operator -- 2.3.4 (1,1)-Extensors, Properties and Associated Extensors -- 2.4 The Metric Clifford Algebra C(V, g) -- The Metric Scalar Product -- The Metric Left and Right Contractions -- The Metric Clifford Product -- 2.5 Pseudo-Euclidean Metric Extensors on V -- 2.5.1 The metric extensor -- 2.5.2 Metric Extensor g with the Same Signature of -- 2.5.3 Some Remarkable Results -- 2.5.4 Useful Identities -- References -- Chapter 3 Multiform Functions and Multiform Functionals -- 3.1 Multiform Functions of Real Variable -- 3.1.1 Limit and Continuity -- 3.1.2 Derivative -- 3.2 Multiform Functions of Multiform Variables -- 3.2.1 Limit and Continuity -- 3.2.2 Differentiability -- 3.2.3 The Directional Derivative AX -- 3.2.4 The Derivative Mapping X -- 3.2.5 Examples -- 3.2.6 The Operators X and their t-distortions -- 3.3 Multiform Functionals F(X1,8230;, Xk)[t] -- 3.3.1 Derivatives of Induced Multiform Functionals -- 3.3.2 The Variational Operator tw -- References -- Chapter 4 Multiform and Extensor Calculus on Manifolds -- 4.1 Canonical Space -- The Position 1-Form -- 4.2 Parallelism Structure (U0,) and Covariant Derivatives -- 4.2.1 The Connection 2-Extensor Field on Uo and AssociatedExtensor Fields -- 4.2.2 Covariant Derivative of Multiform Fields Associated with (U0,) -- 4.2.3 Covariant Derivative of Extensor Fields Associated with (U0,) -- 4.2.4 Notable Identities -- 4.2.5 The 2-Exform Torsion Field of the Structure (Uo,) -- 4.3 Curvature Operator and Curvature Extensor Fields of the Structure (Uo,) -- 4.4 Covariant Derivatives Associated with Metric Structures (Uo, g) -- 4.4.1 Metric Structures -- 4.4.2 Christoffel Operators for the Metric Structure (Uo, g) -- 4.4.3 The 2-Extensor field -- 4.4.4 (Riemann and Lorentz)-Cartan MGSS's (Uo, g,) -- 4.4.5 Existence Theorem of the g-gauge Rotation Extensorof the MCGSS (Uo, g,) -- 4.4.6 Some Important Properties of a Metric Compatible Connection -- 4.4.7 The Riemann 4-Extensor Field of a MCGSS (Uo, g,) -- 4.4.8 Existence Theorem for the on (Uo, g,) -- 4.4.9 The Einstein (1,1)-Extensor Field -- 4.5 Riemann and Lorentz MCGSS's (Uo, g,) -- 4.5.1 Levi-Civita Covariant Derivative -- 4.5.2 Properties of Da -- 4.5.3 Properties of R2(B) and R1(b) -- 4.5.4 Levi-Civita Differential Operators -- 4.6 Deformation of MCGSS Structures -- 4.6.1 Enter the Plastic Distortion Field h -- 4.6.2 On Elastic and Plastic Deformations -- 4.7 Deformation of a Minkowski-Cartan MCGSS into a Lorentz-Cartan MCGSS -- 4.7.1 h-Distortions of Covariant Derivatives -- 4.8 Coupling Between the Minkowski-Cartan and the Lorentz-Cartan MCGSS -- 4.8.1 The Gauge Riemann and Ricci Fields -- 4.8
NotesIncludes bibliographical references and index
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GENERAL RELATIVITY (PHYSICS) 4. GRAVITATION 5. PHYSICS 6. SCIENCE
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