Journal ArticleDOI
Space-Times Admitting Killing-Yano Tensors. II
W. Dietz,R. Rudiger +1 more
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In this paper, the authors derived canonical line elements admitting a simple KillingYano tensor f* ab and showed several close analogies between the vector field la = f * arp r along a geodesic with tangent field p r and the angular momentum l = rxpin the case of a spacelike, timelike and null tensor.Abstract:
In this paper we derive canonical line elements admitting a simple KillingYano tensor f* ab. There exist three distinct cases according to the character o f f* ab (spacelike, timelike, null). We reveal several close analogies between the vector field la = f * arp r along a geodesic with tangent field p r and the angular momentum l = rxpin the case of a spacelike Killing-Yano tensor. In particular, we show that, in consequence of the Killing-Yano tensor equations, there exists an analogue of the three-dimensional position vector field in certain hypersurfaces and th at la can be written in the form (r x p )a. Furthermore, an analogue of the ‘ equatorial plane ’ of the classical Kepler problem can be constructed intrinsically.read more
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The Hidden Symmetries of Multi-Centre Metrics
Gary W. Gibbons,P. J. Ruback +1 more
TL;DR: In this article, the hidden symmetries of the Taub-NUT metric were studied and the results were applied to the scattering of BPS monopoles and fluctuations around such monopoles.
Journal ArticleDOI
Black holes, hidden symmetries, and complete integrability
TL;DR: In this paper, the authors discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-A-dS black hole spacetimes and demonstrate that the principal tensor can be used as a "seed object" which generates all these properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations.
Posted Content
Conformal Killing forms on Riemannian manifolds
TL;DR: Conformal Killing Fields as mentioned in this paper are a generalization of conformal vector fields on Riemannian manifolds, defined as sections in the kernel of a conformally invariant first order differential operator.
Journal ArticleDOI
Hidden Symmetries of Higher-Dimensional Rotating Black Holes
Valeri P. Frolov,David Kubiznak +1 more
TL;DR: In this paper, it was shown that the rotating black holes in an arbitrary number of dimensions possess the same hidden symmetry as the four-dimensional Kerr metric, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.
Journal ArticleDOI
Black holes, hidden symmetries, and complete integrability
TL;DR: It is demonstrated that the principal tensor can be used as a “seed object” which generates all these symmetries of higher-dimensional Kerr–NUT–(A)dS black hole spacetimes and the review contains a discussion of different applications of the developed formalism and its possible generalizations.
References
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Journal ArticleDOI
An Approach to Gravitational Radiation by a Method of Spin Coefficients
Ezra T. Newman,Roger Penrose +1 more
TL;DR: In this paper, a spinor affine connection is proposed for general relativity by means of a tetrad or spinor formalism, which is applied to two problems in radiationtheory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.
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On a quadratic first integral for the charged particle orbits in the charged Kerr solution
TL;DR: In this article, a quadratic first integral of the equation of the motion for charged test particles is derived for the case of the mass of a single particle in the electromagnetic field.
Journal ArticleDOI
On the Relationship between Killing Tensors and Killing-Yano Tensors
TL;DR: In this article, the conditions that a Killing tensor of order 2 be the contracted product of a Killing-Yano tensor with itself with respect to itself were given. And the conditions for admission of all the Killing tensors in order 2 in empty space-times were obtained.
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Intrinsic symmetries in general relativity
TL;DR: In this article, a discussion is presented which indicates that a stagnation point is being reached in the standard applications of symmetries (especially isometries) in general relativity, and an attractive alternative is suggested.
Journal ArticleDOI
Yano vector fields and conformally related spaces
TL;DR: In this article, the authors discuss some geometrical properties of Killing forms of order three and exhibit a procedure for constructing spaces admitting such tensors, and prove that all conformally flat spaces admitting a tensor are related to spaces of constant curvature.