Gravito-magnetic vacuum spacetimes: kinematic restrictions

Ferrando, Joan Josep; Sáez, Juan Antonio

doi:10.1088/0264-9381/20/13/328

Cited by 18 publications

(45 citation statements)

References 12 publications

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“…In the proofs below, we will use that foru a = 0 and h 1 = 0, the diagonal components of (18) reduce to the single equation…”

Section: No-go Results For Pm Rotating Dustmentioning

confidence: 99%

“…Then e.g. the (31) component of the field equations together with 2 1 2 3 and the (31) component of (18) together with the (2) component of (24) Propagation of the second equation of (A.13) along the ∂ 2 integral curves, using (54), (A.12) and (A.13), yields n 1 (4H 13 + z 2 + 4h 3 q 2 ) = 0. As n 1 = 0 is not allowed by (A.13), it follows that B 0 ≡ 4H 13 + z 2 + 4h 3 q 2 = 0.…”

Section: Resultsmentioning

confidence: 99%

“…It follows from the analysis there that for any member of A, an eigenframe B = {u, e α } of σ ab exists, for which (69)-(71) and (73) hold, the shear being degenerate in the (e 2 , e 3 ) plane (h 1 = h 2 + h 3 = 0). Herewith, it follows from (18) and (17) that σ ab , E ab and H ab diagonalize simultaneously in B. Thus the fluid congruence u a is Weyl principal and, as follows from the introduction, purely magnetic (purely electric) spacetimes of A automatically have a PM (PE) Weyl tensor w.r.t.…”

Section: Relaxing the Purely Magnetic Conditionmentioning

confidence: 94%

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Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Wylleman

Bergh

2006

Phys. Rev. D

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Recently the class of purely magnetic non-rotating dust spacetimes has been shown to be empty (Wylleman, Class. Quant. Grav. 23, 2727). It turns out that purely magnetic rotating dust models are subject to severe integrability conditions as well. One of the consequences of the present paper is that also rotating dust cannot be purely magnetic when it is of Petrov type D or when it has a vanishing spatial gradient of the energy density. For purely magnetic and non-rotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D (Lozanovski, Class. Quant. Grav. 19, 6377), the fluid is shown to be non-accelerating if and only if the spatial density gradient vanishes. Under these conditions, a new and algebraically general solution is found, which is unique up to a constant rescaling, which is spatially homogeneous of Bianchi type V I0, has degenerate shear and is of Petrov type I(M ∞ ) in the extended Arianrhod-McIntosh classification.The metric and the equation of state are explicitly constructed and properties of the model are briefly discussed. We finally situate it within the class of normal geodesic flows with degenerate shear tensor.

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“…In the proofs below, we will use that foru a = 0 and h 1 = 0, the diagonal components of (18) reduce to the single equation…”

Section: No-go Results For Pm Rotating Dustmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Relaxing the Purely Magnetic Conditionmentioning

confidence: 94%

See 1 more Smart Citation

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Wylleman

Bergh

2006

Phys. Rev. D

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“…The linearization of E around an FLRW background (26) reads 1 6 ρθσ, such that linearized non-vacuum ID models with E = 0 are either FLRW or satisfy θ = 0, ρ = 2Λ, as is seen from (18). Hence in the case Λ = 0 no linearized anti-Newtonian universes exist at all [7].…”

Section: Purely Magnetic Idmentioning

confidence: 99%

Anti-Newtonian universes do not exist

Wylleman¹

2006

Class. Quantum Grav.

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Abstract. In a paper by Maartens, it was shown that irrotational dust solutions with vanishing electric part of the Weyl tensor are subject to severe integrability conditions and it was conjectured that the only such solutions are FLRW spacetimes. In their analysis the possibility of a cosmological constant Λ was omitted. The conjecture is proved, irrespective as to whether Λ is zero or not, and qualitative differences with the case of vanishing magnetic Weyl curvature are pointed out.

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“…These geometric objects have been under discussion for many years (see [19]- [36] and references therein). Not only because of the eventual relationship of the magnetic part of the Weyl tensor with rotation [20,27], but also because of its link with gravitational radiation [19,23,26,28,29,30,37].…”

Section: Introductionmentioning

confidence: 99%

Energetics of the Einstein–Rosen Spacetime

et al. 2007

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A study covering some aspects of the Einstein-Rosen metric is presented. The electric and magnetic parts of the Weyl tensor are calculated. It is shown that there are no purely magnetic E-R spacetimes, and also that a purely electric E-R spacetime is necessarily static. The geodesics equations are found and circular ones are analyzed in detail. The super-Poynting and the "Lagrangian" Poynting * e-mail: laherrera@cantv.net.ve † e-mail: adiprisc@fisica.ciens.ucv.ve ‡ e-mail: jcarot@uib.es § e-mail: N.O.Santos@qmul.ac.uk and santos@ccr.jussieu.fr 1 vectors are calculated and their expressions are found for two specific examples. It is shown that for a pulse-type solution, both expressions describe an inward radially directed flow of energy, far behind the wave front. The physical significance of such an effect is discussed.2

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Gravito-magnetic vacuum spacetimes: kinematic restrictions

Cited by 18 publications

References 12 publications

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Anti-Newtonian universes do not exist

Energetics of the Einstein–Rosen Spacetime

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