English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We develop a numerical code to compute gravitational waves induced by aparticle moving on eccentric inclined orbits around a Kerr black hole. For suchsystems, the black hole perturbation method is applicable. The gravitationalwaves can be evaluated by solving the Teukolsky equation with a point likesource term, which is computed from the stress-energy tensor of a test particlemoving on generic bound geodesic orbits. In our previous papers, we computedthe homogeneous solutions of the Teukolsky equation using a formalism developedby Mano, Suzuki and Takasugi and showed that we could compute gravitationalwaves efficiently and very accurately in the case of circular orbits on theequatorial plane. Here, we apply this method to eccentric inclined orbits. Thegeodesics around a Kerr black hole have three constants of motion: energy,angular momentum and the Carter constant. We compute the rates of change of theCarter constant as well as those of energy and angular momentum. This is thefirst time that the rate of change of the Carter constant has been evaluatedaccurately. We also treat the case of highly eccentric orbits with $e=0.9$. Toconfirm the accuracy of our codes, several tests are performed. We find thatthe accuracy is only limited by the truncation of $\ell$-, $k$- and $n$-modes,where $\ell$ is the index of the spin-weighted spheroidal harmonics, and $n$and $k$ are the harmonics of the radial and polar motion, respectively. When weset the maximum of $\ell$ to 20, we obtain a relative accuracy of $10^{-5}$even in the highly eccentric case of $e=0.9$. The accuracy is better for lowereccentricity. Our numerical code is expected to be useful for computingtemplates of the extreme mass ratio inspirals, which is one of the main targetsof the Laser Interferometer Space Antenna (LISA).

An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole