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.

Conserved quantities of spinning test particles in general relativity. II

1983 ◽  
Vol 385 (1788) ◽  
pp. 229-239 ◽  
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Conserved Quantities ◽  
Killing Tensor ◽  
Kerr Geometry ◽  
Change Of Variables ◽  
Test Particles ◽  
Suitable Change

In this paper, which completes earlier work on conserved quantities of spinning test particles in general relativity (Rüdiger 1981 a ), quadratic conserved quantities are considered. It is shown that by a suitable change of variables the trivial conserved quantities, which result from a reducible Killing tensor, can essentially be separated from the non-trivial quantities. If the equations of motion are linearized in the spin, it is shown that nontrivial quantities of this type can be constructed for two classes of spacetimes including the Kerr geometry and the Friedman universe.

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 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

scholarly journals Quintom cosmological model and some possible solutions using Lie and Noether symmetries

2016 ◽  
Vol 25 (14) ◽  
pp. 1650110 ◽  
Author(s):  
Sourav Dutta ◽  
Muthusamy Lakshmanan ◽  
Subenoy Chakraborty
Keyword(s):  
Lie Algebra ◽  
Physical System ◽  
Three Dimensional ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Considerable Simplification ◽  
Present Context ◽  
Augmented Space ◽  
Constants Of Motion ◽  
Flrw Universe

The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three-dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence, conserved quantities (i.e. constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.

scholarly journals Adiabatic Evolution of Three 'Constants' of Motion for Greatly Inclined Orbits in Kerr Spacetime

2007 ◽  
Vol 117 (6) ◽  
pp. 1041-1066 ◽  
Author(s):  
K. Ganz ◽  
W. Hikida ◽  
H. Nakano ◽  
N. Sago ◽  
T. Tanaka
Keyword(s):  
Adiabatic Evolution ◽  
Kerr Spacetime ◽  
Constants Of Motion

Dualities and geometrical invariants for static and spherically symmetric spacetimes

2016 ◽  
Vol 25 (09) ◽  
pp. 1641007
Author(s):  
Paola Terezinha Seidel ◽  
Luís Antonio Cabral
Keyword(s):  
General Class ◽  
Hamiltonian Formalism ◽  
Spherically Symmetric ◽  
Conserved Quantities ◽  
Singularity Structure ◽  
Killing Tensors ◽  
Symmetric Spacetimes ◽  
Killing Equation ◽  
Spherically Symmetric Spacetimes ◽  
Spacetime Metric

In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.

On Killing tensors and constants of motion

1973 ◽  
Vol 14 (6) ◽  
pp. 787-790 ◽  
Author(s):  
Paul Sommers
Keyword(s):  
Killing Tensors ◽  
Constants Of Motion
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