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.

Table of Contents

1 Basic Notions

2 Lorentz Connections and Inertia

3 Gauge Theories and Gravitation

4 Fundamentals of Teleparallel Gravity

5 Gravitational Coupling Prescription

6 Particle Mechanics

7 Global Formulation for Gravity

8 Hodge Dual for Soldered Bundles

9 Lagrangian and Field Equations

10 Gravitational Energy-Momentum Density

11 Gravitation in the Lack of Universality

12 Gravitational Coupling of the Fundamental Fields

13 Spin-2 Field Coupled to Gravitation

14 Teleparallel Equivalent of Some Solutions

15 Duality Symmetry

16 Teleparallel Kaluza-Klein Theory

17 Einstein-Cartan Theory

18 Why to Study Teleparallel Gravity

Appendix A The Spinning Particle

Appendix B The Connection Space

Appendix C Teleparallel Field Equation

Appendix D Dirac Equation

Review

“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)