The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity

Capozziello, Salvatore; Capriolo, Maurizio; Transirico, Maria

doi:10.1142/s0219887818501645

Cited by 69 publications

(63 citation statements)

References 43 publications

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“…where subscripts denote derivatives, and Θ ν ρ is the regular energy-momentum tensor. The spin connection is taken to be zero [69,[71][72][73] since this will be a demand in the work that follows. We will revisit this statement at various stages of the analysis to confirm the consistency of the work.…”

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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“…to pseudotensors (not tensors) and not covariant superpotentials, like metric Moller's superpotential, for a detail see Chapter 1 in the book [5]. Recently, in [18] the theories f (R) and f (T ) have been studied and compared. Both of the Lagrangians are Lorentz and coordinate covariant, but the Noether theorem with using invariance with respect to constant coordinate displacements only has been applied.…”

Section: Principle Of Determining Inertial Spin Connectionmentioning

confidence: 99%

“…In [18], the theories f (R) and f (T ) are studied, but the Noether method uses invariance with respect to constant coordinate displacements only. Then, one obtains conserved pseudotensors only, not tensors.…”

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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“…In summary, GWs polarizations are a powerful tool to probe theories of gravity. Moreover, by means of the linearized gravitational energy-momentum pseudo-tensor of f (R), f (T ) gravity [20] or more generally of f (R, R R, . .…”

Section: Introductionmentioning

confidence: 99%

Weak field limit and gravitational waves in f(T, B) teleparallel gravity

2020

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We derive the gravitational waves for f (T, B) gravity which is an extension of teleparallel gravity and demonstrate that it is equivalent to f (R) gravity by linearized the field equations in the weak field limit approximation. f (T, B) gravity shows three polarizations: the two standard of general relativity, plus and cross, which are purely transverse with two-helicity, massless tensor polarization modes, and an additional massive scalar mode with zero-helicity. The last one is a mix of longitudinal and transverse breathing scalar polarization modes. The boundary term B excites the extra scalar polarization and the mass of scalar field breaks the symmetry of the TT gauge by adding a new degree of freedom, namely a single mixed scalar polarization.

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The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity

Cited by 69 publications

References 43 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

Weak field limit and gravitational waves in f(T, B) teleparallel gravity

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