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Teleparallel Gravity

Part of the Fundamental Theories of Physics Book Series (volume 173)

DOI: 10.1007/978-94-007-5143-9

ISBN: 978-94-007-5142-2

Publisher: Springer Netherlands - Springer Journals

Jun 26, 2012

1 - 10 of 18 Chapters

Available

Basic Notions

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 1 –15

[A general spacetime is a 4-dimensional differentiable manifold whose tangent space is, at each point, a Minkowski spacetime. Linear frames and tetrad fields are constitutive parts of its structure as a manifold, and instrumental in relativistic physics and gravitation. They are defined up to...
Available

Lorentz Connections and Inertia

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 17 –23

[In Special Relativity, Lorentz connections represent inertial effects present in non-inertial frames. In these frames, any relativistic equation acquires a manifestly Lorentz covariant form due to the presence of the inertial connection. By virtue of the local equivalence between gravitation and...
Available

Gauge Theories and Gravitation

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 25 –38

[We give here short and rough résumés on gauge models, which describe three of the four fundamental interactions of Nature—and of General Relativity, the standard theory for gravitation, which is not a gauge theory. No more than a “cast of characters”, with only the main protagonists in each...
Available

Fundamentals of Teleparallel Gravity

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 39 –50

[The foundations of Teleparallel Gravity, a gauge theory for the translations group, are presented. The geometrical setting is described, the translational gauge potential introduced, and the notion of gauge transformations explained. The translational coupling prescription is discussed, and the...
Available

Gravitational Coupling Prescription

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 51 –57

[The gravitational coupling prescription is made up of two parts: a translational coupling prescription, which is universal and comes from the translational gauge invariance, and a Lorentz coupling prescription, which is non-universal and comes from the requirement of local Lorentz invariance....
Available

Particle Mechanics

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 59 –72

[The teleparallel force equation is obtained from a variational principle, its equivalence with the geodesic equation is established, and the roles played by torsion and curvature in the descriptions of the gravitational interaction are discussed. The newtonian limit is studied, and the...
Available

Global Formulation for Gravity

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 73 –81

[Due to their shared abelian gauge structure, Teleparallel Gravity and Electromagnetism are similar in several aspects. By analogy to the phase-factor approach to Maxwell’s theory, a teleparallel non-integrable phase-factor formalism for gravitation can be developed. It represents the quantum...
Available

Hodge Dual for Soldered Bundles

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 83 –87

[To account for all possible contractions allowed by the presence of the solder form, a generalized Hodge dual must be defined in the case of soldered bundles. Although for curvature the generalized dual coincides with the usual one, for torsion it gives a new dual definition.]
Available

Lagrangian and Field Equations

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 89 –100

[The lagrangian of Teleparallel Gravity, like those of gauge theories, is quadratic in the field strength—here represented by the torsion tensor. Up to a divergence, it is equivalent to the Einstein-Hilbert lagrangian of General Relativity. The teleparallel field equations, Bianchi identities and...
Available

Gravitational Energy-Momentum Density

Aldrovandi, Ruben; Pereira, José Geraldo

Pages: 101 –110

[In Teleparallel Gravity it is possible to obtain separate expressions for the energy-momentum density of gravity and of the interaction of gravity with inertial effects of the frame. The energy-momentum density of gravity shows up as a true tensor, and satisfies a covariant conservation law. The...

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