Teleparallel theories of gravity as analogue of nonlinear electrodynamics

Hohmann, Manuel; Järv, Laur; Krššák, Martin; Pfeifer, Christian

doi:10.1103/physrevd.97.104042

Cited by 72 publications

(130 citation statements)

References 56 publications

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“…All degrees of freedom are encoded in the tetrad which, in the end, solves the symmetric and the antisymmetric part of the f (T ) field equations, and yields a vanishing torsion scalar in the Minkowski spacetime limit. We like to stress that this is equivalent as considering a non-vanishing spin connection and another tetrad, which together solve symmetric and antisymmetric part of the field equations [27][28][29].…”

Section: Covariant Formulation Of F (T ) Gravity In Spherical Symmentioning

confidence: 99%

“…This is equivalent to having a non-vanishing spin-connection and a tetrad which solve their respective anti-symmetric part of the field equations. A detailed discussion about this equivalence can be found in references [27][28][29].…”

Section: A Covariant Teleparallel Gravitymentioning

confidence: 99%

“…Their symmetric part is sourced by the energy-momentum tensor, while their anti-symmetric part is a vacuum constraint for the matter models we consider. The latter is equal to the variation of the action with respect to the flat spin-connection components [28,29],…”

Section: A Covariant Teleparallel Gravitymentioning

confidence: 99%

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Photon sphere and perihelion shift in weak f(T) gravity

2019

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Among modified theories of gravity, the teleparallel f (T ) gravity is an intensively discussed model in the literature. The best way to investigate its viability is to derive observable predictions which yield evidence or constraints for the model, when compared with actual observations. In this paper we derive the photon sphere and the perihelion shift for weak f (T ) perturbations of general relativity. We consistently calculate first order teleparallel perturbations of Schwarzschild and Minkowski spacetime geometry, with which we improve and extend existing results in the literature. * Electronic address: sbahamonde@ut.ee † Electronic address: kai.flathmann@uni-oldenburg.de ‡ Electronic address: christian.pfeifer@ut.ee

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Section: Covariant Formulation Of F (T ) Gravity In Spherical Symmentioning

confidence: 99%

Section: A Covariant Teleparallel Gravitymentioning

confidence: 99%

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Photon sphere and perihelion shift in weak f(T) gravity

2019

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“…Our principle of defining proper tetrad (the same, of defining A i jµ , could be determined by its own field equations, which just coincide with the antisymmetric part of the field equations. It turns out that all modified teleparallel theories with second order field equations belong the same property, see [33].…”

Section: )mentioning

confidence: 99%

Conserved currents and superpotentials in teleparallel equivalent of GR

Emtsova

Петров²,

Toporensky³

2020

Class. Quantum Grav.

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We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether theorem, we construct new expressions for conserved currents and related superpotentials. They are covariant both under coordinate transformations and local Lorentz rotations, and permit to construct well defined conserved charges, unlike earlier approaches. The advantage is achieved by an explicit presence of a displacement vector in the new expressions that can be interpreted as a Killing vector, as a proper vector of an observer, etc. The new expressions permit to introduce a principle for definition of an inertial spin connection that is undetermined one in the TEGR from the start. Theoretical results are applied to calculate mass for the Schwarzschild black hole and densities of conserved quantities for freely falling observers both in Friedmann-Lemaître-Robertson-Walker world of all the three signs of curvature and in (anti-)de Sitter space.in TEGR feels big difficulties. Particularly these problems are discussed in the book [1], in more detail they are presented in presentation [4] by Martin Krššák. Summating results in previous studies of many authors, he considers conserved energy-momentum complexes and related superpotentials.The Krššák requirements for constructing energy-momentum in TEGR are as follows. It has to 1) be of the first derivatives only, 2) be covariant with respect to both coordinate transformations and local Lorentz rotations, 3) permit to construct global (integral) conserved quantities, or conserved charges, 4) be symmetric and 5) be trace-free. We do not consider the two last requirements as so important. First, it is well known that canonical energy-momentum in a classical field theory is not symmetrical in general, however, it is not a problem for constructing all necessary conserved quantities, see Chapter 1 in the book [5]. Second, the trace-free condition is rather in analogy with the massless electrodynamics. However, we would not provide this analogy as physically so important. Indeed, the electrodynamic field is considered as propagated on fixed or dynamic background spacetime, whereas the gravitational field presents spacetime itself. One could consider perturbations of gravitational field in a given spacetime, however it is not the case that is considered by Krššák [4], and it is not the case that we consider in this paper.The requirement 1) we consider as quite important one, and all variants of energymomentum in TEGR satisfy it. The more interesting and important requirements by Martin Krššák are the requirements 2) and 3). In [4], it is remarked the problem that the known approaches give, on the one hand, well defined conserved charges expressed through well defined surface integrals, but one has only Lorentz non-covariant conserved energy-momentum.On the other hand, one can construct Lorentz covariant conserved energy-momentum, but then it ...

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“…Gauging

T (4)

in the pseudo‐Lorentzian, locally flat manifold, equipped with the acoustic metric and possibly suitable to describe acoustic phonon dynamics, propagation, and interactions, is mathematically not too different from the gauging of

T (4)

on the standard Lorentzian manifold of the General Relativity . Nevertheless, the latter revealed a hard goal to obtain .…”

Section: Challenges In Gauging Spatial Symmetrymentioning

confidence: 99%

Higgs and Goldstone Modes in Crystalline Solids

Vallone

2019

Physica Status Solidi (b)

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In crystalline solids, the acoustic phonon can be described either as a Goldstone or as a non‐Abelian gauge boson. However, the non‐Abelianity of the related gauge group apparently makes the acoustic phonon a frequency‐gapped mode, in contradiction with the other description. In a different perspective, overcoming this contradiction, both acoustic and optical phonon—the latter never appearing following the other two approaches—emerge, respectively, as the gapless Goldstone (phase) and the gapped Higgs (amplitude) fluctuation mode of an order parameter arising from the spontaneous breaking of a global symmetry, without invoking the gauge principle. In addition, the Higgs mechanism describes all the phonon–phonon interactions, including a possible perturbation of the acoustic phonon's frequency dispersion relation induced by the eventual optical phonon, a peculiar behavior that is able to produce mini‐gaps inside the phonon Brillouin zone.

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Teleparallel theories of gravity as analogue of nonlinear electrodynamics

Cited by 72 publications

References 56 publications

Photon sphere and perihelion shift in weak f(T) gravity

Photon sphere and perihelion shift in weak f(T) gravity

Conserved currents and superpotentials in teleparallel equivalent of GR

Higgs and Goldstone Modes in Crystalline Solids

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