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Teleparallel Gravity (TG) is an alternative theory for gravitation, which is equivalent to General Relativity (GR). However, it is conceptually different. For example in GR geometry replaces the concept of force, and the trajectories are determined by geodesics. TG attributes gravitation to torsion, which accounts for gravitation by acting as a force.
TG has already solved some old problems of gravitation (like the energy-momentum density of the gravitational field). The interest in TG has grown in the last few years.
The book here proposed will be the first one dedicated exclusively to TG, and will include the foundations of the theory, as well as applications to specific problems to illustrate how the theory works.
List of contents
From the Content: Basic Notions.- Linear Frames and Tetrads.- Connections.- Gauge Theories and Gravitation.- The Gauge Tenets.- General Relativity.- Gravitation and the Gauge Paradigm.- Fundamentals of Teleparallel Gravity.- Geometrical Setting.- Particle Mechanics.- Free Particles Revisited.- Basic Notions.- Free Equation of Motion.- Global Formulation for Gravity.- Phase Factor Approach.- Colella-Overhauser-Werner Experiment.- Hodge Dual for Soldered Bundles.- Why a New Dual.- Dual Torsion.- Lagrangian and Field Equations.- Lagrangian of Teleparallel Gravity.-Gravitational Energy-Momentum Density.- Field Equations and Conservation Laws.- Teleparallel Gravity.- General Relativity.- Gravitation Without the Equivalence Principle.- Introductory Remarks.- Gravitational Coupling of the Fundamental Fields.- Gravitational Coupling Revisited.- Duality Symmetry.- Duality Symmetry and Gravitation.- Teleparallel Kaluza-Klein Theory.- Kaluza-Klein Theory: a Brief Review.- The Connection Space .- Translations in the Connection Space.- A Glimpse on Einstein-Cartan.- Epilogue.
Summary
Teleparallel Gravity (TG) is an alternative theory for gravitation, which is equivalent to General Relativity (GR). However, it is conceptually different. For example in GR geometry replaces the concept of force, and the trajectories are determined by geodesics. TG attributes gravitation to torsion, which accounts for gravitation by acting as a force.
TG has already solved some old problems of gravitation (like the energy-momentum density of the gravitational field). The interest in TG has grown in the last few years.
The book here proposed will be the first one dedicated exclusively to TG, and will include the foundations of the theory, as well as applications to specific problems to illustrate how the theory works.
Additional text
From the reviews:
“The ideas presented in this book are strongly biased by the authors’ point of view on the subject, and are essentially based on their research output. … It is the first of its kind on TG which includes a study of its foundation and applications to specific problems. … it is worth reading by any researcher in the field of gravitation and torsion.” (Prasanta Mahato, Mathematical Reviews, April, 2013)
“The authors of the present book try to complete the almost exhaustive review article by Hehl et al., updating it by recent research in this area. … the chapters of the book are very useful to any researcher intending to extend his research from the De Sitter space of General Relativity to De Sitter torsioned space, and from the De Sitter-Einstein space to De Sitter-Einstein-Cartan space.” (Alex Gaina, Zentralblatt MATH, Vol. 1259, 2013)
Report
From the reviews:
"The ideas presented in this book are strongly biased by the authors' point of view on the subject, and are essentially based on their research output. ... It is the first of its kind on TG which includes a study of its foundation and applications to specific problems. ... it is worth reading by any researcher in the field of gravitation and torsion." (Prasanta Mahato, Mathematical Reviews, April, 2013)
"The authors of the present book try to complete the almost exhaustive review article by Hehl et al., updating it by recent research in this area. ... the chapters of the book are very useful to any researcher intending to extend his research from the De Sitter space of General Relativity to De Sitter torsioned space, and from the De Sitter-Einstein space to De Sitter-Einstein-Cartan space." (Alex Gaina, Zentralblatt MATH, Vol. 1259, 2013)
