ON CERTAIN GENERALIZATION OF THE CONCEPT OF A SELF-DUAL TENSOR, A HARMONIC TENSOR AND A KILLING TENSOR IN A V.

1969 ◽  
Vol 1 (3) ◽  
pp. 77-138
Author(s):  
Zbigniew Żekanowki
Keyword(s):  
Killing Tensor

scholarly journals PARTICLE DYNAMICS IN WEAKLY CHARGED EXTREME KERR THROAT

2011 ◽  
Vol 20 (05) ◽  
pp. 649-660 ◽  
Author(s):  
A. M. AL ZAHRANI ◽  
VALERI P. FROLOV ◽  
ANDREY A. SHOOM
Keyword(s):  
Charged Particle ◽  
Particle Motion ◽  
Particle Dynamics ◽  
Killing Tensor ◽  
Dynamical Equations ◽  
Kerr Spacetime

We study dynamics of a test charged particle moving in a weakly charged extreme Kerr throat. Dynamical equations of the particle motion are solved in quadratures. We show explicitly that the Killing tensor of the Kerr spacetime becomes reducible in the extreme Kerr throat geometry. Special types of motion of particles and light are discussed.

scholarly journals Complete set of quasi-conserved quantities for spinning particles around Kerr

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Geoffrey Compère ◽  
Adrien Druart
Keyword(s):  
Linear Order ◽  
Conserved Quantities ◽  
Killing Tensor ◽  
Kerr Geometry ◽  
Spinning Particles ◽  
Kerr Spacetime ◽  
Killing Tensors ◽  
Mixed Symmetry ◽  
Constants Of Motion ◽  
Complete Set

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

scholarly journals Killing tensor fields on the 2-torus

2016 ◽  
Vol 57 (1) ◽  
pp. 155-173 ◽  
Author(s):  
V. A. Sharafutdinov
Keyword(s):  
Killing Tensor ◽  
Tensor Fields

scholarly journals Tensor fields associated with integrable systems of chiral

2019 ◽  
Vol 21 (4) ◽  
pp. 405-412
Author(s):  
Alexander V. Balandin
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Necessary Conditions ◽  
Differential Forms ◽  
Type Systems ◽  
Lax Representation ◽  
Killing Tensor ◽  
Tensor Fields ◽  
Linear Differential ◽  
Special Case

This article describes necessary conditions for chiral-type systems to admit Lax representation with values in simple compact Lie algebras. These conditions state that there exists a covariant constant tensor field with an additional property. It is proposed to construct in an invariant way some covariant tensor fields using the Lax representation of the system under consideration. These fields are constructed by taking linear differential forms with values in the Lie algebra that are constructed using the Lax representation of the system and substituting them into an arbitrary Ad-invariant form on the Lie algebra. The paper proves that such tensor fields are Killing tensor fields or covariant constant fields. The discovered necessary conditions for the existence of the Lax representation are obtained using a special case of such tensor fields associated with the Killing metric of the Lie algebra.

scholarly journals Affine Symmetry Tensors in Minkowski Space

2016 ◽  
Vol 13 (3) ◽  
Author(s):  
Isaac Ahern ◽  
Sam Cook
Keyword(s):  
Minkowski Space ◽  
Computational Algorithm ◽  
Minkowski Spacetime ◽  
Lie Derivative ◽  
Killing Tensor ◽  
Spacetime Dimension ◽  
Killing Vectors ◽  
Killing Tensors ◽  
Affine Symmetry

Killing vectors are generators of symmetries in a spacetime. This article defines certain generalizations of Killing vectors, called affine symmetry tensors, or simply affine tensors. While the affine vectors of the Minkowski spacetime are well known, and partial results for valence n = 2 have been discussed, affine tensors of valence n > 2 have never been exhibited. In this article, we discuss a computational algorithm to compute affine tensors in Minkowski spacetime, and discuss the results for affine tensors of valence 2 ≤ n ≤ 7. After comparison with analogous results concerning Killing tensors, we make several conjectures about the spaces of affine tensors in Minkowski spacetime. KEYWORDS: Affine Symmetry Tensors; Affine Vectors; Killing Tensors; Killing Vectors; Minkowski Spacetime; Dimension; Maple CAS; Lie Derivative; Generalized Killing Tensor

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