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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985815%3A_____%2F19%3A00519763" target="_blank" >RIV/67985815:_____/19:00519763 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1088/1361-6382/ab002f" target="_blank" >https://doi.org/10.1088/1361-6382/ab002f</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6382/ab002f" target="_blank" >10.1088/1361-6382/ab002f</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.nThe 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-Semerak 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 Poincare 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 Poincare 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.nThe 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-Semerak 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 Poincare 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 Poincare 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

<a href="/cs/project/GJ17-06962Y" target="_blank" >GJ17-06962Y: Nelineární jevy ve vícekanálové astronomii černých děr</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Classical and Quantum Gravity

ISSN

0264-9381

e-ISSN

1361-6382

Svazek periodika

36

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

31

Strana od-do

075003

Kód UT WoS článku

000460058600003

EID výsledku v databázi Scopus

2-s2.0-85064067618