Covariant differential identities and conservation laws in metric-torsion theories of gravitation. I. General consideration

Lompay, Robert R.; Петров, А. Н.

doi:10.1063/1.4810017

Cited by 15 publications

(13 citation statements)

References 127 publications

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“…The system (3.8) -(3.10) was engineered by Klein, see general and detail discussion in [14,15]. Therefore, we refer to this system as the Klein identities.…”

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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“…The system (3.8) -(3.10) was engineered by Klein, see general and detail discussion in [14,15]. Therefore, we refer to this system as the Klein identities.…”

Section: )mentioning

confidence: 99%

Conserved currents and superpotentials in teleparallel equivalent of GR

Emtsova

Петров²,

Toporensky³

2020

Class. Quantum Grav.

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“…Section 5 discusses two major particular cases: metric and metric-affine backgrounds. In the metric-affine case, the obtained energy-momentum balance law has a simpler (and explicitly covariant) expression compared to the known ones, [13], [12]. The last section presents an application to energy-momentum tensors of the notion of variational completion.…”

Section: Introductionmentioning

confidence: 97%

Energy–momentum tensors in classical field theories — A modern perspective

Voicu

2016

Int. J. Geom. Methods Mod. Phys.

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The paper presents a general geometric approach to energy-momentum tensors in Lagrangian field theories, based on a Hilbert-type definition.The approach is consistent with the ones defining energy-momentum tensors in terms of hypermomentum maps given by the diffeomorphism invariance of the Lagrangian -and, in a sense, complementary to these, with the advantage of an increased simplicity of proofs and also, opening up new insights into the topic. A special attention is paid to the particular cases of metric and metric-affine theories.

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“…Also, Refs. [11] and [12] extensively discussed the diffeomorphically invariant metric-torsion gravity whose action contains first-and second-order derives of the torsion tensor, and derived the full set of Klein-Noether differential identities and various types of conserved currents.…”

Section: Introductionmentioning

confidence: 99%

Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants

Tian

2016

Gen Relativ Gravit

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For a large class of scalar-tensor-like gravity whose action contains nonminimal couplings between a scalar field φ(x α ) and generic curvature invariants {R} beyond the Ricci scalar R = R α α , we prove the covariant invariance of its field equation and confirm/prove the local energy-momentum conservation. These φ(x α ) − R coupling terms break the symmetry of diffeomorphism invariance under a particle transformation, which implies that the solutions to the field equation should satisfy the consistency condition R ≡ 0 when φ(x α ) is nondynamical and massless. Following this fact and based on the accelerated expansion of the observable Universe, we propose a primary test to check the viability of the modified gravity to be an effective dark energy, and a simplest example passing the test is the "Weyl/conformal dark energy".

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Covariant differential identities and conservation laws in metric-torsion theories of gravitation. I. General consideration

Cited by 15 publications

References 127 publications

Conserved currents and superpotentials in teleparallel equivalent of GR

Conserved currents and superpotentials in teleparallel equivalent of GR

Energy–momentum tensors in classical field theories — A modern perspective

Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants

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