'Degenerate' nondegenerate spacetime metrics

McIntosh, C. B. G.; Arianrhod, Robyn

doi:10.1088/0264-9381/7/9/001

Cited by 25 publications

(40 citation statements)

References 2 publications

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“…These classes appear in a natural way when classifying the Bel-Robinson tensor as an endomorphism [7,8]. Moreover, in these spacetimes the four null Debever directions span a 3-plane [6,9,10]. On the other hand, we show that three classes of García-Parrado type I radiative fields can be considered: the IM − , the IM −6 and the generic type I r metrics.…”

Section: Introductionmentioning

confidence: 80%

“…The classification of the Bel-Robinson tensor T as an endomorphism [7,8] leads to nine classes: the Petrov-Bel types O, N , III and II and five subclasses of type I metrics: types I r , IM − , IM −6 , IM + and IM ∞ . These 'degenerate' type I metrics may be characterized in terms of the adimensional Weyl scalar invariant [6,9]:…”

Section: Appendix a Algebraic Classification Of The Bel-robinson Tensormentioning

confidence: 99%

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On the super-energy radiative gravitational fields

Ferrando

Sáez

2013

Class. Quantum Grav.

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We extend our recent analysis (Class. Quantum Grav. 29 075012) on the Bel radiative gravitational fields to the super-energy radiative gravitational fields defined by García-Parrado (Class. Quantum Grav. 25 015006). We give an intrinsic characterization of the new radiative fields, and we consider some distinguished classes of both radiative and non radiative fields. Several super-energy inequalities are improved.

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Section: Introductionmentioning

confidence: 80%

Section: Appendix a Algebraic Classification Of The Bel-robinson Tensormentioning

confidence: 99%

On the super-energy radiative gravitational fields

Ferrando

Sáez

2013

Class. Quantum Grav.

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“…This way, it is known [14,20] that the cases where M is real positive or infinity, which are called IM + or IM ∞ respectively, correspond to the case of the Weyl eigenvalues having a real ratio ( ρ i ρ j is a real number; the case M = ∞ means that the Weyl tensor has a vanishing eigenvalue). An equivalent condition in terms of Debever null directions has also been obtained [14,20]: M is real positive or infinity if, and only if, the four Debever null directions span a 3-plane.…”

Section: Labeling Some Weyl Types With the Main Br Scalar Invariantsmentioning

confidence: 99%

“…On the other hand, the main BR scalars also distinguish between five classes of algebraically general Weyl tensors. These classes refine the Petrov-Bel classification and were introduced by McIntosh and Arianrhod [14]. They correspond to particular configurations of the four null principal directions: either they span a 3-plane or they define a frame with permutability properties.…”

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confidence: 96%

On the algebraic types of the Bel–Robinson tensor

Ferrando

Sáez

2008

Gen Relativ Gravit

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The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov-Bel types and the additional ones are intrinsically characterized in terms of the sole Bel-Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.

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“…the quadratic, cubic and 0-dimensional invariants I, J and M of the Weyl tensor [7,8] can be written as [1,9] …”

Section: Introductionmentioning

confidence: 99%

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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'Degenerate' nondegenerate spacetime metrics

Cited by 25 publications

References 2 publications

On the super-energy radiative gravitational fields

On the super-energy radiative gravitational fields

On the algebraic types of the Bel–Robinson tensor

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

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