On the covariance of teleparallel gravity theories

Golovnev, Alexey; Koivisto, Tomi S.; Sandstad, Marit

doi:10.1088/1361-6382/aa7830

Cited by 184 publications

(234 citation statements)

References 27 publications

(59 reference statements)

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“…However, works exist in the literature that consider this scenario such as Refs. [14,78] where a Palatini approach is considered so that a second set of field equations are produced for the spin connection.…”

Section: Teleparallel Gravity and Its Extension To F (T B) Gravitymentioning

confidence: 99%

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

2020

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Gravitomagnetism characterize phenomena in the weak field limit within the context of rotating systems. These are mainly manifested in the geodetic and Lense-Thirring effects. The geodetic effect describes the precession of the spin of a gyroscope in orbit about a massive static central object, while the Lense-Thirring effect expresses the analogous effect for the precession of the orbit about a rotating source. In this work, we explore these effects in the framework of Teleparallel Gravity and investigate how these effects may impact recent and future missions. We find that teleparallel theories of gravity may have an important impact on these effects which may constrain potential models within these theories.

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Section: Teleparallel Gravity and Its Extension To F (T B) Gravitymentioning

confidence: 99%

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

2020

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“…In spite of that the Moller Lagrangian (2.5) and the TEGR Lagrangian Last time a great attention arises to extended variants of teleparallel gravity. The most popular is f (T ) theories, see [7,26,27,28,29,30,31,32] and references there in. 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.…”

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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“…One such possibility is the use of the Palatini approach to implement the flat, metric-compatible connection [27]. Another approach, which is the one we will make use of here, is the covariant formulation, which features an arbitrary, flat, metric-compatible spin connection [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories

Emtsova

Hohmann

2020

Phys. Rev. D

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We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is non-minimally coupled to the torsion of a flat, metric-compatible connection. This class of scalar-torsion theories of gravity is constructed in analogy to and as a direct extension of the well-studied class of scalar-curvature gravity theories, and has various common features, such as the conformal frame freedom. For this class we determine the parametrized post-Newtonian limit, both for a massive and a massless scalar field. In the massive case, we determine the effective gravitational constant and the post-Newtonian parameter γ, both of which depend on the distance between the gravitating and test masses. In the massless case, we calculate the full set of parameters and find that only γ and β potentially deviate from their general relativity values. In particular, we find that for a minimally coupled scalar field the theory becomes indistinguishable from general relativity at this level of the post-Newtonian approximation.

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On the covariance of teleparallel gravity theories

Cited by 184 publications

References 27 publications

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

Conserved currents and superpotentials in teleparallel equivalent of GR

Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories

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