Energy-momentum conservation in gravity theories

Bak, Dongsu; Cangemi, Daniel; Jackiw, R.

doi:10.1103/physrevd.49.5173

Cited by 113 publications

(125 citation statements)

References 22 publications

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“…Another interesting application seems to be the class of models in 3 (or 5 and higher odd dimensions) with topological terms included in the Lagrangian. The case of a 3-dimensional gravity theory of that type was earlier studied in [12], where the corresponding conserved quantities were explicitly derived. The complete analysis of this class of models will be given elsewhere.…”

Section: Discussionmentioning

confidence: 99%

“…However, the Lagrangian may be shifted by a total derivative term (equivalently, by a boundary term). This actually happens in many gravitational field models: (i) when one adds a noninvariant boundary term to the original Lagrangian, (ii) when the gravitational dynamics is described in the purely tetrad framework [1], (iii) when the Lagrangian includes topological terms (e.g., of the Chern-Simons type [4 -6]), typically in 3 and 5 dimensions, for example [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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

2006

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Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a diffeomorphism on the spacetime. We further generalize previous results for the case of gravitational models described by quasi-invariant Lagrangians, that is, Lagrangians that change by a total derivative under the action of the local Lorentz group. The general formalism is then applied to the teleparallel models, for which the energy and the angular momentum of a Kerr black hole are calculated. The subsequent analysis of the results obtained demonstrates the importance of the choice of the frame.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2006

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“…Therefore, as a residual symmetry, we obtain translations, local in time, and rigid rotations (see also [30][31][32] for a similar situation in General Relativity). Putting (4.8) and (4.11) into the Chern-Simons action (see (3.5) and (3.11)) we find (modulo a total time derivative)…”

Section: Gauge Fixing and Residual Symmetrymentioning

confidence: 99%

From Gauging Nonrelativistic Translations to N-Body Dynamics

Lukierski

Stichel²,

Zakrzewski

2001

Annals of Physics

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We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gaugeinvariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d × (d + 1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d = 2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in * e-mail: lukier@ift.uni.wroc.pl † email: pstichel@gmx.de ‡ e-mail: W.J.Zakrzewski@durham.ac.uk 1 time) translations and rigid rotations. We describe the effective interaction of the d = 2 N -particle problem and discuss its classical solution for N = 2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H = H( x, p; H) which implies, after quantization, a nonstandard form of the Schrödinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r ≤ r 0 ) and the scattering states with continuum energy correspond to the classical motion for r > r 0 . We extend our considerations by introducing an external constant magnetic field and, for N = 2, provide the classical and quantum solutions in the confined and unconfined regimes.

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“…This leaves of course a lot of freedom in the definition of these forms, and allows one to show for instance that the expressions derived in [12,1,2,8] for energy-momentum and angular momentum in asymptotically flat general relativity are all equivalent (see also e.g. [13] for a recent discussion).…”

Section: Introductionmentioning

confidence: 99%

“…In the Einstein-Maxwell example, solutions to (13) are given by the Killing vectors of the background metric, Lξḡ µν = 0, which satisfy in addition LξĀ µ + ∂ µλ = 0 for some gauge parameterλ. In the case of trivial topology, equation (14) implies that sf = d Hkf , for some n − 2 formkf [ϕ;φ].…”

Section: Introductionmentioning

confidence: 99%

Boundary charges in gauge theories: using Stokes theorem in the bulk

Barnich¹

2003

Class. Quantum Grav.

147

206

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Boundary charges in gauge theories (like the ADM mass in general relativity) can be understood as integrals of linear conserved n-2 forms of the free theory obtained by linearization around the background. These forms are associated one-to-one to reducibility parameters of this background (like the time-like Killing vector of Minkowski space-time). In this paper, closed n-2 forms in the full interacting theory are constructed in terms of a one parameter family of solutions to the full equations of motion that admits a reducibility parameter. These forms thus allow one to apply Stokes theorem without bulk contributions and, provided appropriate fall-off conditions are satisfied, they reduce asymptotically near the boundary to the conserved n-2 forms of the linearized theory. As an application, the first law of black hole mechanics in asymptotically anti-de Sitter space-times is derived.

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Energy-momentum conservation in gravity theories

Cited by 113 publications

References 22 publications

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

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

From Gauging Nonrelativistic Translations to N-Body Dynamics

Boundary charges in gauge theories: using Stokes theorem in the bulk

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