Selected topics in teleparallel gravity
TL;DR: In this paper, it was shown that the fundamental field of teleparallel gravity is not the tetrad nor the metric, but a gauge potential assuming values in the Lie algebra of the translation group.
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Abstract: Teleparallel gravity can be seen as a gauge theory for the translation group. As such, its fundamental field is neither the tetrad nor the metric, but a gauge potential assuming values in the Lie algebra of the translation group. This gauge character makes of teleparallel gravity, despite its equivalence to general relativity, a rather peculiar theory. A first important point is that it does not rely on the universality of free fall, and consequently does not require the equivalence principle to describe the gravitational interaction. Another peculiarity is its similarity with Maxwell's theory, which allows an Abelian nonintegrable phase factor approach, and consequently a global formulation for gravitation. Application of these concepts to the motion of spinless particles, as well as to the COW and gravitational Aharonov-Bohm effects are presented and discussed.
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Citations
Static Anisotropic Solutions in f(T) Theory
TL;DR: In this article, a spherically symmetric solution for the static and anisotropic content in f(T) theory was obtained, considering a constant torsion and some particular conditions for the pressure.
201
Static Anisotropic Solutions in f(T) Theory
TL;DR: In this article, a spherically symmetric solution was obtained for the general case of an isotropic fluid and for the anisotropic content case in which the generalized conditions for the matter content were considered such that the energy density, the radial and tangential pressures depend on the algebraic function and its derivative.
159
Regular black holes in $f(T)$ Gravity through a nonlinear electrodynamics source
TL;DR: In this article, a new class of exact solutions of regular black holes in f(T) gravity with non-linear electrodynamics material content, with spherical symmetry in 4D, was obtained.
135
Solar System tests in f(T) gravity
TL;DR: In this article, the authors investigated the four solar system tests of gravity (perihelion precession, light bending, Shapiro time delay, and redshift) in a non-nondiagonal vierbein field for a polynomial $f(T)$ gravity, and derived the solutions for each test, in which Weinberg's, Bodenner and Will's, Cattani et al., and Rindler and Ishak's methods are applied.
120
Newton–Cartan theory and teleparallel gravity: The force of a formulation
TL;DR: In this article, it is shown that the ontological commitments of general relativity and teleparallel gravity cannot be directly deduced from their mathematical form, and that the spacetime geometry involved in a gravity theory is not a straightforward consequence of anything internal to that theory as a theory of gravity.
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References
•Book
An Introduction to Geometrical Physics
Ruben Aldrovandi,José Geraldo Pereira +1 more
- 01 Dec 1995
TL;DR: Manifolds tangent structure differential forms symmetries fibre bundles topical sections - mathematics as mentioned in this paper, mathematics, physics, science, and technology. But this paper is not related to our work.
The classical theory of fields
TL;DR: The principle of relativity Relativistic mechanics Electromagnetic fields electromagnetic waves as discussed by the authors The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation