Magnetic curvatures

Arianrhod, Robyn; Lun, A. W. C.; McIntosh, C. B. G.; Perjés, Zoltán

doi:10.1088/0264-9381/11/9/014

Cited by 26 publications

(47 citation statements)

References 8 publications

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“…n 22 , resp. n 33 , one gets equations h 20 1 h 5 2 h 5 3 P (h 2 , h 3 )n 16 22 = h 20 1 h 5 2 h 5 3 P (h 2 , h 3 )n 16 33 = 0, with P (h 2 , h 3 ) a homogeneous polynomial of its arguments, such that n 22 = n 33 = 0 by lemma 4.1 (c). Hence n 1 = n 2 = n 3 = 0, in contradiction with (53).…”

Section: Resultsmentioning

confidence: 98%

“…In [18,19] the non-existence of shear-free or non-rotating PM models was generalized to spacetimes with a vanishing Cotton tensor. As a positive example on the other hand, the metric constructed in [20] turns out to be a PM kinematic counterpart to the Gödel metric [21], but its source is unphysical as the Ricci tensor is of Segré type [11,ZZ]. In [22], PM locally rotationally symmetric (LRS) spacetimes were shown to belong to either class I or III of the Stewart-Ellis classification [23], the possible Segré-types were determined and the most general metric forms were found, exhibiting one arbitrary function and three parameters.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Wylleman

Bergh

2006

Phys. Rev. D

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“…In [22], an exact solution of Einstein's field equations with E ab = 0 = H ab is found, apparently the first such solution. The solution is given in the form (reversing the signature to conform with our convention)…”

Section: Appendix B a Purely Gravito-magnetic Solutionmentioning

confidence: 96%

“…are Newman-Penrose null vectors (using the notationṽ = v a dx a ). The Segre type of the nonzero Ricci tensor is given in [22] as {1 1 zz}, but no further discussion is given of the properties of (B9). We find that u = −x −1 du − xdy , which impliesũ ∧ dũ = 2x −1 du ∧ dx ∧ dy = 0 .…”

Section: Appendix B a Purely Gravito-magnetic Solutionmentioning

confidence: 99%

“…An exact non-vacuum solution is given in [22], apparently the first purely gravito-magnetic solution. However, as pointed out in [22], this solution has unphysical Segre type. We show in an appendix that it is kinematically a magnetic counterpart of the Gödel solution (which is purely gravito-electric [5]), but that dynamically it has an unphysical source, with negative energy density.…”

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confidence: 99%

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Newtonian-like and anti-Newtonian universes

Maartens

Lesame

Ellis

1998

Class. Quantum Grav.

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In an irrotational dust universe, the locally free gravitational field is covariantly described by the gravito-electric and gravito-magnetic tensors E ab and H ab . In Newtonian theory, H ab = 0 and E ab is the tidal tensor. Newtonian-like dust universes in general relativity (i.e. with H ab = 0, often called 'silent') have been shown to be inconsistent in general and unlikely to extend beyond the known spatially homogeneous or Szekeres examples. Furthermore, they are subject to a linearization instability. Here we show that 'anti-Newtonian' universes, i.e. with purely gravito-magnetic field, so that E ab = 0 = H ab , are also subject to severe integrability conditions. Thus these models are inconsistent in general. We show also that there are no anti-Newtonian spacetimes that are linearized perturbations of Robertson-Walker universes. The only E ab = 0 = H ab solution known to us is not a dust solution, and we show that it is kinematically Gödel-like but dynamically unphysical.PACS numbers: 0420, 9880, 9530 IntroductionIrrotational dust spacetimes are characterized by vanishing pressure (p = 0) ‡ and vorticity (ω a = 0), and positive energy density (ρ > 0). They are important arenas for studying both the late universe [1,2] and gravitational collapse models [3]. Apart from the spatially homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) case, which is characterized by vanishing shear (σ ab = 0), these spacetimes have non-zero shear and non-zero locally free gravitational field. This field is represented by the irreducible electric and magnetic parts E ab and H ab of the Weyl tensor (see [4] for a covariant analysis of local freedom in the gravitational field). ‡ It is implicit that the anisotropic stress π ab and the energy flux q a also vanish. § A weaker covariant condition for the absence of gravitational radiation is that the spatial curls (defined below) of E ab and H ab must vanish [7,8,4].

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Irrotational dust with a purely magnetic Weyl tensor

Lesame

1995

Gen Relat Gravit

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Magnetic curvatures

Cited by 26 publications

References 8 publications

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Newtonian-like and anti-Newtonian universes

Irrotational dust with a purely magnetic Weyl tensor

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