New Properties of Euclidean Killing Tensors of Rank Two

2019 ◽  
Vol 51 ◽  
pp. 1-7
Author(s):  
Mircea Crasmareanu ◽  
Keyword(s):  
Killing Tensors

scholarly journals Killing tensors on tori

2017 ◽  
Vol 117 ◽  
pp. 1-6
Author(s):  
Konstantin Heil ◽  
Andrei Moroianu ◽  
Uwe Semmelmann
Keyword(s):  
Killing Tensors

Generalized Killing Tensors

2000 ◽  
Vol 32 (9) ◽  
pp. 1767-1776 ◽  
Author(s):  
C. D. Collinson ◽  
L. Howarth
Keyword(s):  
Killing Tensors

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.

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