{"title":"Gravitational Wave Modeling of Extreme Mass Ratio Inspirals Perturbed by an Outer Supermassive Black Hole","authors":"Abdeldjalil Zaidi, Sofiane Aoudia","doi":"10.1134/S0202289321030142","DOIUrl":null,"url":null,"abstract":"<p>We apply the method of osculating orbits in the Schwarzschild–Droste space-time using the relativistic orbital evolution equations for a perturbed extreme mass ratio inspiral (EMRI) by an outer supermassive black hole. The latter supposedly lies in the orbital plane, so that the orbital elements related to inclination and ascending node do not play a role. Our approach encompasses both strong and weak gravity fields. For calculating the gravitational waveforms of perturbed EMRIs through the Regge–Wheeler–Zerilli wave equations, we apply the second-order source-free integration method. Designed for integration in the time domain, our algorithm consists of a finite difference scheme that discretizes the space-time into a grid cell <span>\\((t,r^{*})\\)</span>, whereas the discontinuity of the gravity field at the world line of the particle is dealt with jump conditions on the wave function and its derivatives.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"27 3","pages":"247 - 268"},"PeriodicalIF":1.2000,"publicationDate":"2021-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289321030142","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
We apply the method of osculating orbits in the Schwarzschild–Droste space-time using the relativistic orbital evolution equations for a perturbed extreme mass ratio inspiral (EMRI) by an outer supermassive black hole. The latter supposedly lies in the orbital plane, so that the orbital elements related to inclination and ascending node do not play a role. Our approach encompasses both strong and weak gravity fields. For calculating the gravitational waveforms of perturbed EMRIs through the Regge–Wheeler–Zerilli wave equations, we apply the second-order source-free integration method. Designed for integration in the time domain, our algorithm consists of a finite difference scheme that discretizes the space-time into a grid cell \((t,r^{*})\), whereas the discontinuity of the gravity field at the world line of the particle is dealt with jump conditions on the wave function and its derivatives.
期刊介绍：
Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community
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