Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity

Obukhov, Yuri N.; Rubilar, Guillermo F.; Pereira, J. G.

doi:10.1103/physrevd.74.104007

Cited by 36 publications

(50 citation statements)

References 27 publications

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“…[25,26]. Teleparallel gravity has been readdressed by Obukhov and Pereira [27] in the geometrical framework of metric-affine theories, and further reconsidered by Obukhov and Rubilar [28,29], with the purpose of investigating the transformation (covariance) properties and conserved currents in tetrad theories of gravity. They analysed the problem of consistently defining the gravitational energy-momentum and, in particular, the problem of regularization of the expression of the gravitational energy-momentum (see also Ref.…”

Section: Review Articlementioning

confidence: 99%

The teleparallel equivalent of general relativity

2013

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A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space-time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.

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Section: Review Articlementioning

confidence: 99%

The teleparallel equivalent of general relativity

2013

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“…(8), (12), and (27)] from various generalizations of Killing vectors, defined as the respective solutions to Eqs. (7), (11), and the system given by Eqs. (26) and (29), which can in principle be constructed in generic spacetimes.…”

Section: Discussionmentioning

confidence: 99%

“…A more detailed investigation, which I leave for future work, will involve the further study of the systems (in particular their solutions in various spacetime geometries) described in Eqs. (7), (11) and Eqs. (26), (29).…”

Section: Discussionmentioning

confidence: 99%

“…One potentially useful example is a vector field of the form 1 Note that there is a gauge freedom in this definition; for a torsionfree connection ∇µ, J µ K is invariant under the transformation U µ → U µ + ∇ µ σ (σ being a scalar field). 2 I also refer the reader to [5] and related work which extend the analysis to more general theories of gravity [6][7][8].∇ µ φ, which is divergence free if the scalar field satisfies the wave equation φ = 0. From the Komar current J µ K , I may construct the 3form:By Stokes' theorem, the integral of the above over some constant-time hypersurface Σ t becomes:where dΣ µ and dS µν are the respective surface elements 3 for Σ t and ∂Σ t .…”

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Some globally conserved currents from generalized Killing vectors and scalar test fields

Feng

2018

Phys. Rev. D

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In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an identically vanishing divergence. I obtain some expressions for Komar currents constructed from some generalizations of Killing vectors which may in principle be constructed in a generic spacetime. I then present an explicit example for an outgoing Vaidya spacetime which demonstrates that the resulting Komar currents can yield conserved quantities that behave in a manner expected for the energy contained in the outgoing radiation. Finally, I describe a method for constructing another class of (non-Komar) globally conserved currents using a scalar test field that satisfies an inhomogeneous wave equation, and discuss two examples; the first example may provide a useful framework for examining the arrow of time and its relationship to energy conditions, and the second yields (with appropriate initial conditions) a globally conserved energy-and momentumlike quantity that measures the degree to which a given spacetime deviates from symmetry. I. THE KOMAR CURRENTIn a 1959 article [1], Arthur Komar presented a globally conserved current (the Komar current) for general relativistic spacetimes, which is constructed from an arbitrary vector field U µ (which serves as the generator for diffeomorphisms). The Komar current is of the form: 1(1)The Komar current has theoretical appeal because it can be derived from the action in the context of Noether's theorem-in [2][3][4], it was shown that the Komar current is in fact the conserved current corresponding to the diffeomorphism invariance of the Einstein-Hilbert Lagrangian coupled to matter. 2 Using the Ricci identity [∇ µ , ∇ ν ]T αβ = R α σµν T σβ + R β σµν T ασ for the Levi-Civita connection ∇ µ , it is straightforward to show that the divergence of J µ K identically vanishes:The above result is an identity for any quantity of the form given in Eq. (1); it only depends on the Ricci identity for rank-2 tensors. Note also that Eq. (2) permits a shift freedom in J µ K ; any divergence-free vector added to J µ K preserves the divergence-free property Eq. (2). One potentially useful example is a vector field of the form 1 Note that there is a gauge freedom in this definition; for a torsionfree connection ∇µ, J µ K is invariant under the transformation U µ → U µ + ∇ µ σ (σ being a scalar field). 2 I also refer the reader to [5] and related work which extend the analysis to more general theories of gravity [6][7][8].∇ µ φ, which is divergence free if the scalar field satisfies the wave equation φ = 0. From the Komar current J µ K , I may construct the 3form:By Stokes' theorem, the integral of the above over some constant-time hypersurface Σ t becomes:where dΣ µ and dS µν are the respective surface elements 3 for Σ t and ∂Σ t . Equation (4) may be used to construct quasilocal expressions for quantities associated with a Komar current. Note in a close...

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“…Sharif and Nazir (2008) found that energymomentum turns out to be the same in TEGR and GR for Bell-Szekeres metric. Some people (de Andrade et al 2000;Obukhov and Pereira 2003;Obukhov et al 2006;Lucas et al 2009) proposed a new concept in this regard: "Lagrangian framework in TEGR". In this framework, Maluf et al (2002) defined gravitational energy, momentum and angular momentum using the literature (Maluf 1994).…”

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confidence: 98%

Energy contents of some rotating spacetimes in teleparallel gravity

Sharif

Jawad

2010

Astrophys Space Sci

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The present work is devoted to elaborate energymomentum problem using the integral form of the constraint equations in the Hamiltonian formulation of teleparallel equivalent to general relativity. This approach is used to evaluate energy and its related quantities for LewisPapapetrou spacetimes, spatially homogeneous rotating spacetimes and their special cases. The results of energy are compared with those already found using different prescriptions. We conclude that energy distribution for these spacetimes do not coincide in general with those already available in literature. We also evaluate gravitational and matter energy-momentum flux.

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Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity

Cited by 36 publications

References 27 publications

The teleparallel equivalent of general relativity

The teleparallel equivalent of general relativity

Some globally conserved currents from generalized Killing vectors and scalar test fields

Energy contents of some rotating spacetimes in teleparallel gravity

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