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  Hamiltonians and canonical coordinates for spinning particles in curved space-time

Witzany, V., Steinhoff, J., & Lukes-Gerakopoulos, G. (2019). Hamiltonians and canonical coordinates for spinning particles in curved space-time. Classical and Quantum Gravity, 36(7): 075003. doi:10.1088/1361-6382/ab002f.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-FA45-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-333D-0
Genre: Journal Article

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Witzany, Vojtěch, Author
Steinhoff, Jan1, Author              
Lukes-Gerakopoulos, Georgios, Author
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1Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1933290              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE,
 Abstract: The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the so-called Effective-One-Body waveform models that should eventually cover all mass ratios. The MPD equations require supplementary conditions determining the frame in which the moments of the body are computed. We review various choices of these supplementary spin conditions and their properties. Then, we give Hamiltonians either in proper-time or coordinate-time parametrization for the Tulczyjew-Dixon, Mathisson-Pirani, and Kyrian-Semer\'ak conditions. Finally, we also give canonical phase-space coordinates parametrizing the spin tensor. We demonstrate the usefulness of the canonical coordinates for symplectic integration by constructing Poincar\'e surfaces of section for spinning bodies moving in the equatorial plane in Schwarzschild space-time. We observe the motion to be essentially regular for EMRI-ranges of the spin, but for larger values the Poincar\'e surfaces of section exhibit the typical structure of a weakly chaotic system. A possible future application of the numerical integration method is the inclusion of spin effects in EMRIs at the precision requirements of LISA.

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 Dates: 2018-08-2020192019
 Publication Status: Published in print
 Pages: 19 pages, 2 figures. Submitted to Phys. Rev. D
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 Identifiers: arXiv: 1808.06582
URI: http://arxiv.org/abs/1808.06582
DOI: 10.1088/1361-6382/ab002f
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Title: Classical and Quantum Gravity
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Pages: - Volume / Issue: 36 (7) Sequence Number: 075003 Start / End Page: - Identifier: -