Komar fluxes of circularly polarized light beams and cylindrical metrics

Lynden-Bell, D.; Bičák, Jiřı́

doi:10.1103/physrevd.96.104053

Cited by 12 publications

(14 citation statements)

References 27 publications

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“…It could be worthwhile to see whether a similar solution for the gravitational field of a focused laser beam as we derived in this article could be derived considering the full coupled set of the Einstein-Maxwell equations. The resulting metric could be compared to the one in [21] and it could be investigated if the results of [21] about the effective gravitating mass and angular momentum can be reproduced when divergence of the beam is taken into account. It would also be interesting to consider the gravitational field of the electromagnetic field distribution used in this article to model a focused laser beam in dynamical spacetime theories with spacetime torsion like Einstein-Cartan-Theory and the Poincaré-Gauge-Theory of gravity [18].…”

Section: Discussionmentioning

confidence: 99%

The gravitational field of a laser beam beyond the short wavelength approximation

Schneiter

Rätzel

Braun

2018

Class. Quantum Grav.

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Light carries energy, and therefore, it is the source of a gravitational field. The gravitational field of a beam of light in the short wavelength approximation has been studied by several authors. In this article, we consider light of finite wavelengths by describing a laser beam as a solution of Maxwell's equations and taking diffraction into account.Then, novel features of the gravitational field of a laser beam become apparent, such as frame-dragging due to its spin angular momentum and the deflection of parallel co-propagating test beams that overlap with the source beam.Even though the effects are too small to be detected with current technology, they are of conceptual interest, revealing the gravitational properties of light.

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Section: Discussionmentioning

confidence: 99%

The gravitational field of a laser beam beyond the short wavelength approximation

Schneiter

Rätzel

Braun

2018

Class. Quantum Grav.

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“…The quantity Q therefore behaves in a manner expected for the energy contained in a uniform pulse of radiation emitted by a spherical object, except that the change in the charge δQ ∼ 2δM is twice the expected value. The factor of two here comes from the fact that the energy-momentum tensor for the Vaidya spacetime is trace-free; it was noted in [11] that Komar integrals for trace-free energy-momentum tensors yield values twice that of energy-momentum tensors with nonvanishing trace. The results I obtain here further establishes those of [11].…”

Section: An Example: the Vaidya Spacetimementioning

confidence: 99%

“…The factor of two here comes from the fact that the energy-momentum tensor for the Vaidya spacetime is trace-free; it was noted in [11] that Komar integrals for trace-free energy-momentum tensors yield values twice that of energy-momentum tensors with nonvanishing trace. The results I obtain here further establishes those of [11].…”

Section: An Example: the Vaidya Spacetimementioning

confidence: 99%

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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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“…Actually, there has existed a lot of literature involved in its modifications and generalizations. For example, see the works [5,6,7,8,9,10,11,12,13,14,15,16,17]. As another example to construct conserved currents expected to provide interesting insights into the conventional Komar current, let us take into consideration of its extension corresponding to an exact symmetry generated by the Killing vector fields.…”

Section: Introductionmentioning

confidence: 99%

Generalized Komar currents for vector fields

Peng¹,

Zou²

2019

Preprint

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In this paper, on basis of three quadratic differential operators leaving the form degree of an arbitrary differential form unchanged, that is, the d'Alembertian operator and two combined ones from the Hodge coderivative and the exterior derivative, the usual Komar current for a Killing vector is formulated into another equivalent form. Then it is extended to more general currents in the absence of the linearity in the Killing vector field. Moreover, motivated by this equivalent of the usual Komar current, we put forward a conserved current corresponding to a generic vector with some constraint. Such a current can be generalized to the one with higher-order derivatives of the vector. The applications to some specific vector fields, such as the almost-Killing vectors, the conformal Killing vectors and the divergence-free vectors, are investigated. It is demonstrated that the above generalizations of the Killing vector can be uniformly described by a second-order derivative equation.

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Komar fluxes of circularly polarized light beams and cylindrical metrics

Cited by 12 publications

References 27 publications

The gravitational field of a laser beam beyond the short wavelength approximation

The gravitational field of a laser beam beyond the short wavelength approximation

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

Generalized Komar currents for vector fields

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