Alignment and Algebraically Special Tensors in Lorentzian Geometry

Milson, Robert; Coley, A. A.; Pravda, Vojtěch; Pravdová, Alena

doi:10.1142/s0219887805000491

Cited by 125 publications

(354 citation statements)

References 12 publications

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“…7 In the frame (79), from (81) one finds the only non-zero components F 1ij ∼ 1/r 2 , in agreement with (75). It may be interesting also to observe that the field (81) is self-dual (or anti-self-dual) if its only non-zero components are…”

Section: Examples For N = 6 P =supporting

confidence: 80%

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Asymptotic behavior of Maxwell fields in higher dimensions

Ortaggio

2014

Phys. Rev. D

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We study the fall-off behaviour of test electromagnetic fields in higher dimensions as one approaches infinity along a congruence of "expanding" null geodesics. The considered backgrounds are Einstein spacetimes including, in particular, (asymptotically) flat and (anti-)de Sitter spacetimes. Various possible boundary conditions result in different characteristic fall-offs, in which the leading component can be of any algebraic type (N, II or G). In particular, the peelingoff of radiative fields F = N r 1−n/2 + Gr −n/2 + . . . differs from the standard four-dimensional one (instead it qualitatively resembles the recently determined behaviour of the Weyl tensor in higher dimensions). General p-form fields are also briefly discussed. In even n dimensions, the special case p = n/2 displays unique properties and peels off in the "standard way" as F = N r 1−n/2 + IIr −n/2 + . . .. A few explicit examples are mentioned.

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Section: Examples For N = 6 P =supporting

confidence: 80%

“…w.r.t. ℓ (i.e., decreasing alignment [7] -the G abcd term is not aligned and is thus "generic"). Similarly, for the Maxwell field one has (both for test fields in flat space [6,8,9] and for the full Einstein-Maxwell theory [6])…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of Maxwell fields in higher dimensions

Ortaggio

2014

Phys. Rev. D

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“…Therefore, from now on we refer to the off-shell spacetime (4.1), without imposing (4.3), as to the canonical metric. The canonical metric is of the special algebraic type D [102] of the higher-dimensional algebraic classification [178], [46], [45]. Let us finally remark that formulas (4.1)- (4.3) are applicable also in D = 3 where one recovers the 2-parametric BTZ black hole [13].…”

Section: Overview Of the Kerr-nut-(a)ds Metricsmentioning

confidence: 98%

“…These solutions allow the Kerr-Schild form [185], they are of the type D of the higher-dimensional algebraic classification [178], [46], [45]. The metrics have slightly different form for the odd and even number of spacetime dimensions D. We can write them compactly as…”

Section: B1 Myers-perry Metrics and Their Symmetriesmentioning

confidence: 99%

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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In this thesis we study higher-dimensional rotating black holes. Such black holes are widely discussed in string theory and brane-world models at present.We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime, describing the general rotating higher-dimensional asymptotically (anti) de Sitter black hole with NUT parameters, is in many aspects similar to its fourdimensional counterpart. Namely, we show that it admits a fundamental hidden symmetry associated with the principal conformal Killing-Yano tensor. Such a tensor generates towers of hidden and explicit symmetries. The tower of Killing tensors is responsible for the existence of irreducible, quadratic in momenta, conserved integrals of geodesic motion. These integrals, together with the integrals corresponding to the tower of explicit symmetries, make geodesic equations in the Kerr-NUT-(A)dS spacetime completely integrable. We further demonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, and stationary string equations allow complete separation of variables and the problem of finding parallel-propagated frames reduces to the set of the first order ordinary differential equations. Moreover, we show that the Kerr-NUT-(A)dS spacetime is the most general Einstein space which possesses all these properties. We also explicitly derive the most general (off-shell) canonical metric admitting the principal conformal Killing-Yano tensor and demonstrate that such a metric is necessarily of the special algebraic type D of the higher-dimensional algebraic classification. The results presented in this thesis describe the new and complete picture of the relationship of hidden symmetries and rotating black holes in higher dimensions. PrefaceWhen in 1963 Kerr discovered an astrophysically relevant but relatively complicated metric describing the gravitational field of a rotating black hole, it seemed that no analytical predictions were possible even for the simplest particle geodesic motion. However, a 'miracle' happened, and it turned out that not only the geodesic motion can be analytically solved, but also the equations describing various perturbations of this background can be 'drastically' simplified. This opened a way for studying astrophysical processes, such as the plasma accretion around black holes, the radiation produced by infalling matter, the origin of jets, the production and propagation of waves produced in the vicinity of black holes, and it even led to estimates of the gravitational wave production in star collisions and galaxy merges. It also facilitated the study of more theoretical problems, such as the problem of stability of the Kerr solution, the calculation of the quasinormal modes, or the study of the Hawking radiation. A hidden symmetry responsible for this miracle can be mathematically described by a simple antisymmetric object, called the Killing-Yano tensor.Recently, higher-dimensional rotating black hole spacetimes have become of high interest due to various developments in gravity and high energy physic...

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“…, C 1i1j are subject to a number of constraints following from additional symmetries of the Weyl tensor and its tracelessness [1,2]. Boost order of a tensor T is defined as the maximum boost weight of its frame components and it can be shown that it depends only on the choice of a null direction ℓ [1,2]. Boost order of the Weyl tensor in a generic case is 2, but in algebraically special cases, there exist preferred null directions for which boost order of the Weyl tensor is less.…”

Section: Peeling Property Of the Weyl Tensormentioning

confidence: 99%