On the Weyl transverse frames in type I spacetimes

Ferrando, Joan Josep; Sáez, Juan Antonio

doi:10.1007/s10714-005-0087-y

Cited by 4 publications

(9 citation statements)

References 14 publications

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“…We can find a similar situation in type D spacetimes where some families determined by imposing conditions on the gradient of the Weyl eigenvalue turn out to be those classes defined attending the geometric properties of the Weyl principal structure [29]. The above result for the case of type I metrics leads us to the following classification [7]:…”

Section: Type I Metrics With Vanishing Cotton Tensor: Generalized Sze...mentioning

confidence: 88%

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Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

Ferrando

Sáez

2003

Class. Quantum Grav.

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Abstract. We analyze type I vacuum solutions admitting an isometry whose Killing 2-form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group G 3 of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2-form are also determined. The SzekeresBrans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.

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Section: Type I Metrics With Vanishing Cotton Tensor: Generalized Sze...mentioning

confidence: 88%

“…We also offer an invariant subclassification of the type I 1 metrics and prove that the classes can be characterized by the Bianchi type of the G 3 . Some of these results were communicated without proof at the Spanish Relativity Meeting 1998 [7].…”

Section: Introductionmentioning

confidence: 99%

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

Ferrando

Sáez

2003

Class. Quantum Grav.

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“…This is in fact a preferable alternative, as it means elimination of the "puregauge" longitudinal-wave effects. Notably, [46] presented a covariant procedure, applicable to any type-I spacetime and any initially chosen NP tetrad, how to find a new tetrad (the transverse frame) in which Ψ 1 = 0 and Ψ 3 = 0, together with prescriptions for the new values of Ψ 0 , Ψ 2 and Ψ 4 . Such an option seems ideal for our projections (66)-(69) of the MPD equations, since they do not contain Ψ 0 and Ψ 4 from the beginning, so their values are irrelevant.…”

Section: Ideally Rotated Np Tetrads: Transverse Framesmentioning

confidence: 99%

“…Such an option seems ideal for our projections (66)-(69) of the MPD equations, since they do not contain Ψ 0 and Ψ 4 from the beginning, so their values are irrelevant. Hence, if we used in our picture as k µ and l µ the vectors reached in Corollary 2 of [46] (and derive V µ , e µ î from them accordingly), the MPD-equation projections (66)-(69) would reduce to the type-D form (86)-(89) in any field. The only exception is type III where the "transverse" frame cannot be found; the existence and (non-)uniqueness of such a tetrad were summarized in [44].…”

Section: Ideally Rotated Np Tetrads: Transverse Framesmentioning

confidence: 99%

“…There is a problem, however: as found in [46], there generally exist three distinct "principal" transverse frames (k µ , l µ , m µ , mµ ), plus a continuous set of their derivatives obtained by renormalization e φ k µ , e −φ l µ in the real time-like plane and rotation e −iθ m µ , e iθ mµ in the complex space-like plane. Hence, for any of these alternatives, the (k µ , l µ ) plane is fixed, so -like with the Kinnersley-tetrad choice in the type-D case -it is not in general possible to fix it to the spin direction concurrently.…”

Section: Ideally Rotated Np Tetrads: Transverse Framesmentioning

confidence: 99%

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Spinning particles in vacuum spacetimes of different curvature types

Semerák

Šrámek

2015

Phys. Rev. D

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We consider the motion of spinning test particles with nonzero rest mass in the "pole-dipole" approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary condition added to close the system. The MPD equation of motion is decomposed in the orthonormal tetrad whose time vector is given by the four-velocity $V^\mu$ chosen to fix the spin condition (the "reference observer") and the first spatial vector by the corresponding spin; such projections do not contain the Weyl scalars $\Psi_0$ and $\Psi_4$ obtained in the associated Newman-Penrose (NP) null tetrad. One natural choice of the remaining two spatial basis vectors is shown to follow "intrinsically"; it is realizable if the particle's four-velocity and four-momentum are not parallel. To see how the problem depends on the curvature type, one first identifies the first vector of the NP tetrad $k^\mu$ with the highest-multiplicity principal null direction of the Weyl tensor, and then sets $V^\mu$ so that $k^\mu$ belong to the spin-bivector eigenplane. In spacetimes of any algebraic type but III, it is possible to rotate the tetrads so as to become "transverse", namely so that $\Psi_1$ and $\Psi_3$ vanish. If the spin-bivector eigenplane could be made coincide with the real-vector plane of any of such transverse frames, the motion would consequently be fully determined by $\Psi_2$ and the cosmological constant; however, this can be managed in exceptional cases only. Besides focusing on specific Petrov types, we derive several sets of useful relations valid generally and check whether/how the exercise simplifies for some specific types of motion. The particular option of having four-velocity parallel to four-momentum is advocated and a natural resolution of nonuniqueness of the corresponding reference observer $V^\mu$ is suggested.Comment: 20 pages, no figure

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Gravito-magnetic vacuum spacetimes: kinematic restrictions

Ferrando¹,

Sáez²

2003

Class. Quantum Grav.

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We show that there are no vacuum solutions with a purely magnetic Weyl tensor with respect to an observer submitted to kinematic restrictions involving first order differential scalars. This result generalizes previous ones for the vorticity-free and shear-free cases. We use a covariant approach which makes evident that only the Bianchi identities are used and, consequently, the results are also valid for non vacuum solutions with vanishing Cotton tensor.

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On the Weyl transverse frames in type I spacetimes

Cited by 4 publications

References 14 publications

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

Spinning particles in vacuum spacetimes of different curvature types

Gravito-magnetic vacuum spacetimes: kinematic restrictions

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