A simple prescription for computing the stress - energy tensor

Accioly, Antonio; Azeredo, Abel Dionizio; Aragão, Cristiane Moura Lima de; Mukai, H.

doi:10.1088/0264-9381/14/5/019

Cited by 10 publications

(27 citation statements)

References 10 publications

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“…ik is proportional to the corresponding term in [15], the part T (3) ik reproduces the stress-energy tensor of [16]. The tensor T (2) ik is new.…”

Section: Non-minimal Constitutive Equationsmentioning

confidence: 99%

“…The Lagrangian of such a theory contains the three U(1) gauge-invariant scalars R ikmn F ik F mn , R ik g mn F im F kn and RF mn F mn with coefficients proportional to the square of the Compton wavelength of the electron. Subsequently, a non-minimal coupling of gravity and electromagnetism has been discussed by a number of authors in different settings [8,9,10,11,12,13,14,15,16,17,18]. Non-minimally extended theories were used as a framework to discuss potential limitations of the equivalence principle [19,20,21]).…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic cosmological models with nonminimally coupled magnetic field

Balakin

Zimdahl

2005

Phys. Rev. D

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Motivated by the structure of one-loop vacuum polarization effects in curved spacetime we discuss a non-minimal extension of the EinsteinMaxwell equations. This formalism is applied to Bianchi I models with magnetic field. We obtain several exact solutions of the non-minimal system including those which describe an isotropization process. We show that there are inflationary solutions in which the cosmological constant is determined by the non-minimal coupling parameters. Furthermore, we find an isotropic de Sitter solution characterized by a "screening" of the magnetic field as a consequence of the non-minimal coupling.

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“…ik is proportional to the corresponding term in [15], the part T (3) ik reproduces the stress-energy tensor of [16]. The tensor T (2) ik is new.…”

Section: Non-minimal Constitutive Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anisotropic cosmological models with nonminimally coupled magnetic field

Balakin

Zimdahl

2005

Phys. Rev. D

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“…Refs. [28][29][30][31][32][33][34][35][36][37][38][39]. Reference 38 revived, as well, the interest in the paradigm: curvature coupling and equivalence principle, various aspects of which are being discussed (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Analogous feature can be found in the nonminimal model described above [see Eq. (35)]. Indeed, the quantity K with the dimensionality of squared frequency (c = 1) can be regarded as an analog of Ω 2 p , and the quantity 2(6q 1 + 3q 2 + q 3 ) can be indicated as 1/ω 2 ; then the term 1 − 2K(6q 1 + 3q 2 + q 3 ) plays the role of effective permittivity scalar ε q .…”

mentioning

confidence: 99%

Nonminimal Isotropic Cosmological Model With Yang–mills and Higgs Fields

Balakin

Dehnen

Zayats

2008

Int. J. Mod. Phys. D

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We establish a nonminimal Einstein-Yang-Mills-Higgs model, which contains six coupling parameters. The first three parameters relate to the nonminimal coupling of a non-Abelian gauge field and a gravity field, the next two parameters describe the so-called derivative nonminimal coupling of a scalar multiplet with a gravity field, and the sixth parameter introduces the standard coupling of a scalar field with a Ricci scalar. The formulated six-parameter nonminimal Einstein-Yang-Mills-Higgs model is applied to cosmology. We show that there exists a unique exact cosmological solution of the de Sitter type for a special choice of the coupling parameters. The nonminimally extended Yang-Mills and Higgs equations are satisfied for arbitrary gauge and scalar fields, when the coupling parameters are specifically related to the curvature constant of the isotropic space-time. Based on this special exact solution, we discuss the problem of a hidden anisotropy of the Yang-Mills field, and give an explicit example, when the nonminimal coupling effectively screens the anisotropy induced by the Yang-Mills field and thus restores the isotropy of the model.

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“…We denote arbitrary matter fields by ψ A ; the signature of the metric g µν is chosen to be (− + ++); the expressions ∇ µ f and f ;µ both denote covariant derivation relative to the metric g µν and we set c = 8πG = 1. In accordance with [1], we assume that pure gravitation is described by the usual Einstein-Hilbert Lagrangian, although the considerations below hold, mutatis mutandis, under more general assumptions. The matter Lagrangian is L(g, ψ) = L(g µν , R λ µνσ , ψ A , ψ A;µ ): the dependence on g includes a possible non-minimal coupling to the curvature.…”

mentioning

confidence: 99%

Can the Local Energy-Momentum Conservation Laws be Derived Solely from Field Equations?

Magnano¹,

Sokołowski²

1998

General Relativity and Gravitation

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Abstract. The vanishing of the divergence of the matter stress-energy tensor for General Relativity is a particular case of a general identity, which follows from the covariance of the matter Lagrangian in much the same way as (generalized) Bianchi identities follow from the covariance of the purely gravitational Lagrangian. This identity, holding for any covariant theory of gravitating matter, relates the divergence of the stress tensor with a combination of the field equations and their derivatives. One could thus wonder if, according to a recent suggestion [1], the energy-momentum tensor for gravitating fields can be computed through a suitable rearrangement of the matter field equations, without relying on the variational definition. We show that this can be done only in particular cases, while in general it leads to ambiguities and possibly to wrong results. Moreover, in nontrivial cases the computations turn out to be more difficult than the standard variational technique.In a recent paper [1] Accioly et al. have observed that for some well known cases of classical fields interacting with gravitation (e.g. scalar field, electromagnetic field), upon contracting the dynamical equation for the matter field with a suitable linear combination of covariant derivatives of this field, the resulting expression represents the vanishing of the covariant 4-divergence of some rank-two tensor. In the cases considered in [1], the latter turns out to coincide exactly with the stress-energy tensor of the matter field, according to the usual variational definition.Let us explain the geometrical origin of this phenomenon. For the reader's convenience, we recall the derivation of the strong conservation law (sometimes called "Bianchi identity for matter") in the case of metric theories of gravity, in the form suitable for our aim. We denote arbitrary matter fields by ψ A ; the signature of the metric g µν is chosen to be (− + ++); the expressions ∇ µ f and f ;µ both denote covariant derivation relative to the metric g µν and we set c = 8πG = 1. In accordance with [1], we assume that pure gravitation is described by the usual Einstein-Hilbert Lagrangian, although the considerations below hold, mutatis mutandis, under more general assumptions. The matter Lagrangian is L(g, ψ) = L(g µν , R λ µνσ , ψ A , ψ A;µ ): the dependence on g includes a possible non-minimal coupling to the curvature. The resulting action is S = Ω

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A simple prescription for computing the stress - energy tensor

Abstract: A non-variational technique for computing the stress-energy tensor is presented. The prescription is used, among other things, to obtain the correct field equations for Prasanna's highly nonlinear electrodynamics.

Cited by 10 publications

References 10 publications

Anisotropic cosmological models with nonminimally coupled magnetic field

Anisotropic cosmological models with nonminimally coupled magnetic field

Nonminimal Isotropic Cosmological Model With Yang–mills and Higgs Fields

Can the Local Energy-Momentum Conservation Laws be Derived Solely from Field Equations?

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