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Gravitation as a plastic distortion of the Lorentz vacuum. (English) Zbl 1205.83003

Fundamental Theories of Physics 168. Berlin: Springer (ISBN 978-3-642-13588-0/hbk; 978-3-642-26485-6/pbk; 978-3-642-13589-7/ebook). x, 153 p. (2010).
This book presents a view to gravitation which interprets it as a distortion of special relativity. In the introduction, the usual concepts of differential geometry are introduced, including torsion and non-metricity. They are then related to symmetries and conservation laws. In section 2, the metric Clifford algebra and related objects are presented in detail. Sections 3 and 4 present a lot of material on multiform and extensor calculus on manifolds.
Section 5 is the core of the book, its title “Gravitation as plastic distortion of the Lorentz vacuum” is almost identical to the title of the whole book. It shows how with the methods of the previous sections, gravitational field equations can be derived in a flat Minkowski background. By the way, this idea has already a long history, these theories are often called “bimetric theories of gravitation”. The next two sections apply the results of section 5 to the wave equation for the metric, energy, and conservation laws for matter. The seven appendices explain some further differential geometry used within the main text.
The theory described in this book is different from Einstein’s general relativity theory. Due to its construction, it assumes a global \({\mathbb{R}}^4\)-topology for the whole spacetime from the beginning, thus excluding objects like black holes and closed cosmological models known from Einstein’s general relativity theory.

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C40 Gravitational energy and conservation laws; groups of motions
83A05 Special relativity
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83E05 Geometrodynamics and the holographic principle
15A66 Clifford algebras, spinors
53Z05 Applications of differential geometry to physics
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C25 Approximation procedures, weak fields in general relativity and gravitational theory

Keywords:

torsion
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