Gravitation as a plastic distortion of the Lorentz vacuum

Gravitation as a plastic distortion of the Lorentz vacuum [electronic resource] / Virginia Velma Fernández, Waldyr A. Rodrigues, Jr.

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Fernández, Virginia Velma
Other Authors: Rodrigues, W. A.
Format: Electronic eBook
Language:English
Published: Berlin ; Heidelberg ; New York : Springer-Verlag, ©2010.
Series:Fundamental theories of physics ; v. 168.
Subjects:
Gravitation.
Table of Contents:
  • Cover13;
  • 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.

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