| Description |
1 online resource (x, 153 pages) |
| Series |
Fundamental theories of physics ; v. 168 |
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Fundamental theories of physics ; v. 168.
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| 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 |
| Summary |
Addressing graduate students and researchers in theoretical physics and mathematics, this book presents a new formulation of the theory of gravity. In the new approach the gravitational field has the same ontology as the electromagnetic, strong, and weak fields. In other words it is a physical field living in Minkowski spacetime. Some necessary new mathematical concepts are introduced and carefully explained. Then they are used to describe the deformation of geometries, the key to describing the gravitational field as a plastic deformation of the Lorentz vacuum. It emerges after further analysis that the theory provides trustworthy energy-momentum and angular momentum conservation laws, a feature that is normally lacking in General Relativity |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Gravitation.
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Gravitation
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SCIENCE -- Waves & Wave Mechanics.
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Physique.
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Gravitation
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| Form |
Electronic book
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| Author |
Rodrigues, W. A
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| ISBN |
9783642135897 |
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3642135897 |
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