Covariant differential identities and conservation laws in metric-torsion theories of gravitation. II. Manifestly generally covariant theories

Lompay, Robert R.; Петров, А. Н.

doi:10.1063/1.4826478

Cited by 11 publications

(16 citation statements)

References 57 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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“…Of particular importance is the diffeomorphism (or general coordinate) invariance of the action (39). Substituting (1), (2), (3), and (32) into (45), we recast the latter (after dropping the overall infinitesimal constant ǫ) into…”

Section: A Lagrange-noether Analysismentioning

confidence: 99%

Invariant conserved currents in generalized gravity

et al. 2015

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We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to non-Riemannian spacetime geometry and nonminimal coupling. We demonstrate that an arbitrary vector field on the spacetime manifold generates a current density that is conserved under certain conditions, and find the expression of the corresponding superpotential. For a family of models including nonminimal coupling between geometry and matter, we discuss in detail the differential conservation laws and the conserved quantities defined in terms of covariant multipole moments. We show that the equations of motion for the multipole moments of extended microstructured test bodies lead to conserved quantities that are closely related to the conserved currents derived in the field-theoretic framework.Comment: 15 pages, RevTex format. arXiv admin note: text overlap with arXiv:1505.0168

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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. II. Manifestly generally covariant theories

Cited by 11 publications

References 57 publications

Conserved currents and superpotentials in teleparallel equivalent of GR

Conserved currents and superpotentials in teleparallel equivalent of GR

Invariant conserved currents in generalized gravity

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

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