Comparing Hamiltonians of a spinning test particle for different tetrad fields
Kunst, D., Ledvinka, T., Lukes-Gerakopoulos, G., Seyrich, J.
This work is concerned with suitable choices of tetrad fields and coordinate systems for the Hamiltonian formalism of a spinning particle derived in [E. Barausse, E. Racine, and A. Buonanno, Phys. Rev. D 80,
104025 (2009)]. After demonstrating that with the originally proposed tetrad field the components of the total angular momentum are not preserved in the Schwarzschild limit, we analyze other hitherto proposed
tetrad choices. Then, we introduce and thoroughly test two new tetrad fields in the horizon penetrating Kerr–Schild coordinates. Moreover, we show that for the Schwarzschild spacetime background the linearized in spin Hamiltonian corresponds to an integrable system, while for the Kerr spacetime we find chaos which suggests a nonintegrable system.
| type: | article |
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| journal: | Phys. Rev. D |
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| volume: | 93 |
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| pages: | 044004 |
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| year: | 2016 |
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| eprint: | arxiv:1506.01473 |
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| grants: | General relativistic fields of compact astrophysical sources, GAČR 14-10625S; 2014-2016; hlavní řešitel: Oldřich SemerákVýzkum Země a vesmíru metodami teoretické, počítačové a experimentální fyziky; 2012-2017; řešitelé: David Vokrouhlický, Marek Wolf, Oldřich Semerák |
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