Comparing Hamiltonians of a spinning test particle for different tetrad fields

Kunst, Daniela; Ledvinka, Tomáš; Lukes-Gerakopoulos, Georgios; Seyrich, Jonathan

doi:10.1103/physrevd.93.044004

Cited by 21 publications

(42 citation statements)

References 57 publications

(116 reference statements)

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“…Consequently, an analogous special planar motion P ϑ =ẋ ϑ = S µϑ = 0 would in fact have only a single active degree of freedom under the NW condition and would thus be integrable at any value of spin. Additionally, even the non-planar motion under the NW Hamiltonian of Barausse et al [10] is integrable to linear order in S in Schwarzschild space-time, at least under the right choice of ξ µ [39]. Hence, the chaos found in our study using the KS condition is a qualitatively different feature as compared to a treatment using the NW condition.…”

Section: Comparison With Previous Resultscontrasting

confidence: 53%

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

Witzany

Steinhoff

Lukes-Gerakopoulos

2019

Class. Quantum Grav.

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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 socalled 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-Semerák 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 Poincaré 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 Poincaré 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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Section: Comparison With Previous Resultscontrasting

confidence: 53%

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

Witzany

Steinhoff

Lukes-Gerakopoulos

2019

Class. Quantum Grav.

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“…To compare K R with K so , one simply needs to substitute the spin-perturbed four-velocity into (43), and a somewhat involved computation yields…”

Section: Interpretation Of Separation Constantsmentioning

confidence: 99%

Hamilton-Jacobi equation for spinning particles near black holes

Witzany

2019

Phys. Rev. D

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A compact stellar-mass object inspiralling onto a massive black hole deviates from geodesic motion due to radiation-reaction forces as well as finite-size effects. Such post-geodesic deviations need to be included with sufficient precision into wave-form models for the upcoming space-based gravitational-wave detector LISA. I present the formulation and solution of the Hamilton-Jacobi equation of geodesics near Kerr black holes perturbed by the so-called spin-curvature coupling, the leading order finite-size effect. In return, this solution allows to compute a number of observables such as the turning points of the orbits as well as the fundamental frequencies of motion. This result provides one of the necessary ingredients for waveform models for LISA and an important contribution useful for the relativistic two-body problem in general.

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“…However, when MPD are linearized in spin, it appears that under certain conditions they are approximately separable [18]. It is unclear whether this means that chaos and prolonged resonances do not appear at linear order in spin [19,20]. Whether spin-induced chaos and resonances play any role in EMRI needs yet to be determined in order to make accurate predictions for LISA waveforms.…”

Section: Introductionmentioning

confidence: 99%

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

et al. 2020

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Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear.We numerically integrate the motion of a spinning test body in the field of a non-spinning black hole and analyse it using various methods. We show for the first time that resonances and chaos can be found even for astrophysical values of spin. On the other hand, we devise a method to analyse the growth of the resonances, and we conclude that the resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the small-mass-ratio limit. Last but not least, we compute gravitational waveforms by solving numerically the Teukolsky equations in the time-domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source.

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Comparing Hamiltonians of a spinning test particle for different tetrad fields

Cited by 21 publications

References 57 publications

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

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

Hamilton-Jacobi equation for spinning particles near black holes

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

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